Sequence and Series

If the sum of '$n$' terms of an AP (Arithmetic Progression) is $2n^2$, the fifth term is ____.

The sum of first $n$ terms an AP is $3n^2+5n$. The series is:

If $2+6+10+14+.........+x=882$ then the value of $x$ is

If the sum of five terms of AP is $75$. Find the third term of the series.

The $20^{th}$ term of arithmetic progression whose $6^{th}$ term is $38$ and $10^{th}$ term is $66$ is:

Divide $69$ into $3$ parts which are in A.P. and are such that the product of first two parts is $483$.

The number of terms of the series: $5+7+9+...$ must be taken so that the sum may be $480$.

A person pays $975$ in monthly installments, each installment is less than formed by $5$. The amount of $1^{st}$ installment is $100$. In what time will the entire amount be paid?

If the sum of $n$ terms of an AP is $(3n^2-n)$ and its common difference is $6$, then its $1^{st}$ term is:

Insert two arithmetic means between $68$ and $260$.

If the $p^{th}$ term of an A.P. is '$q$' and the $q^{th}$ term is '$p$', then its $n^{th}$ term is

The sum of the series $-8,-6,-4,.........n$ terms is $52$. The number of terms $n$ is

The value of $K$, for which the terms $7K+3, 4K-5, 2K+10$ are in A.P., is

If $p^{th}$ term of an AP is $q$ and its $q^{th}$ term is $p$, then what will be the value of $(p+q)^{th}$ term?

How many numbers between $74$ and $25,556$ are divisible by $5$?

If $9^{th}$ and $19^{th}$ term of an AP are $35$ and $75$, respectively, then its $20^{th}$ term is:

Find the $17^{th}$ term of an AP series if $15^{th}$ and $21^{st}$ terms are $30.5$ and $39.5$ respectively.

If $n^{th}$ term of an AP series is $7n-2$, then sum of '$n$' terms is:

Find the value of '$x$' for the following data $1+7+13+19.........+x=225$

If fourth term of A.P. series is zero, then what is the ratio of twenty-fifth term of eleventh term?

If $8^{th}$ term of an AP is $15$, the Sum of the $15$ its term is

For what value of $x$; the sequence $x+1, 3x, 4x+2$ are in AP?

The $n^{th}$ element of the series $3,5,7,...$ is

If $1+3+5+.........+n$ terms $= \frac{n^2}{2}$ If $2+4+6+.........+50$ terms $= 51$ then the value of '$n$' is

If $6^{th}$ and $13^{th}$ term of an A.P are $15$ and $36$ respectively the A.P is

The value of $K$, for which the terms $7K+3$, $4K-5$, $2K+10$ are in A.P., is

The first term of an A.P. is $100$ and the sum of whose first $6$ terms is $5$ times the sum of the next $6$ terms, then the c.d. is:

The sum of $n$ terms of an A.P. is $3n^2+n$; then its $p^{th}$ term is

If three AM's between $3$ and $11$, they are

The first and the last term of an AP are $-4$ and $146$. The sum of the terms is $7171$. The number of terms is

The sum of the first $3$ terms in an AP is $18$ and that of the last $3$ is $28$. If the AP has $13$ terms, find sum of the middle three terms?

The ratio of sum of first $n$ natural numbers to sum of cubes of first $n$ natural numbers is

Sum of progression $(a+b)$, $(a-b)$, $(a-3b)...n$ term is

Find the sum of first twenty-five terms of A.P. series whose $n^{th}$ term is $\left(n+\frac{2}{5}\right)$

Insert $4$ A.M.'s between $3$ and $18$:

The first and fifth term of an A.P. of $40$ terms are $-29$ and $-15$ respectively. Find the sum of all positive terms of this A.P

If the common difference of an AP equals to the first term, then the ratio of its $m^{th}$ term and $n^{th}$ term is:

Find the value of $1+2+3+...+105$

The $n^{th}$ term of the series $9,7,5,...$ and $15,12,9,...$ are same. Find the $n^{th}$ term?

If the ratio of sum of $n$ terms of two APs is $(n-1):(n+1)$, then the ratio of their $n^{th}$ terms is

In an arithmetic progression, the seventh terms is $x$, and $(x+7)^{th}$ term is zero. Then $x^{th}$ term is

If the second and eight terms of an arithmetic progression (AP) are equal to constant $a$, then the sum of first $n$ terms of this AP is equal to

The $3^{rd}$ term of arithmetic progression is $7$ and Seventh term is $2$ more than thrice of third term. The common difference is

Which term of the AP $64, 60, 56, 52...$ is $0$

If the sum of $n$ terms of an AP is $2n^2$, then $5^{th}$ term is

Sum up to infinity of series. $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{8} + \frac{1}{9} + \frac{1}{16} + \frac{1}{27} + \dots$

Sum the series $\frac{1}{5} + \frac{1}{5^2} + \frac{1}{5^3} + \dots + \frac{1}{5^n}$

Find no. of terms of the series $25, 5, 1, \dots, \frac{1}{3125}$

Three numbers in G.P. with their sum 130 and their product 27,000 are:

In a geometric progression, that $3^{rd}$ and $6^{th}$ terms are respectively 1 and $-1/8$. The term $(a)$ and common ratio are respectively.

If the sum and product of three numbers in G.P. are 7 and 8 respectively, then $4^{th}$ term of the series is

The $3^{rd}$ term of a G.P. is $2/3$ and the $6^{th}$ term is $2/81$ then the $1^{st}$ term is

The sum of series $7 + 14 + 21 + \dots$ to $17^{th}$ term is:

The largest value of $n$ for which $1 + \frac{1}{2} + \frac{1}{2^2} + \dots + \frac{1}{2^{n-1}} < 0.998$ is

The sum of first 8 terms of a G.P is five times the sum of the first 4 terms. Find the common ratio?

In a GP $5^{th}$ term is 27 and $8^{th}$ term is 729. Find its $11^{th}$ term?

If $4^{th}, 7^{th}$ and $10^{th}$ terms of a Geometric Progression are $p, q$ and $r$, respectively, then:

Given an infinite geometric series with first term '$a$' and common ratio '$r$'. If its sum is 4 and the second term is $\frac{3}{4}$, then one of correct option is

If for an infinite geometric progression, first term is '$a$', common ratio is '$r$', the sum is 8 and the second term is $\frac{7}{8}$, then

For what values of $X$, the number $\frac{-2}{7}, X, \frac{-7}{2}$ are in G.P.?

If the sum of $n$ terms of an AP is $3n^2-n$ and its common difference is $6$, then its $1^{st}$ term is

Sum lying from $100$ to $300$ which is divisible by $4$ and $5$ is

Sum of $n$ terms of two AP's are in the ratio $(3n+5):(5n+3)$ then ratio of their $10^{th}$ term

If the $p^{th}$ term of an A.P. is 'q' and the $q^{th}$ term is 'p', then its $r^{th}$ term is:

In AP $T_p=q$ and $T_q=p$ then $T_{p+q}=$

If the sum of $n$ terms of an A.P. be $2n^2+5n$, then its '$n^{th}$' term is:

If $20$ AMs. are inserted between $3$ and $51$ then sum of these $20$ A.M.s is

The first, second and seventh term of an AP are in G.P. and the common difference is $2$, the $2^{nd}$ term of A.P. is:

The $4^{th}$ term of an A.P. is three times the first and the $7^{th}$ term exceeds twice the third term by $1$. Find the first term 'a' and common difference 'd'.

Find the sum of all natural numbers betn $250$ and $1000$ which are exactly divisible by $3$:

A person puts Rs. $975$ in monthly instalment, each instalment is less than former by Rs. $5$. The amount of first instalment is Rs. $100$. In what time will the entire amount be paid?

If the sum of $n$ terms of an A.P. is $(3n^2-n)$ and its common difference is $6$, then its first term is:

If $(x+1)$, $3x$, $(4x+2)$ are in A.P. Find the value of $x$

Divide 144 into three parts which are in AP and such that the largest is twice the smallest, the smallest of three numbers will be:

If $8^{th}$ term of an AP is 15, the sum of the 15 terms is

For what value of $x$, the sequence $x+1, 3x, 4x+2$ are in AP?

The $n^{th}$ term of the series whose sum to $n$ terms is $3n^2+2n$ is

In a G.P., if the fourth term is '3' then the product of first seven terms is

$y = 1 + x + x^2 + \dots \infty$, then $x =$

Find the three numbers in G.P. whose sum is 19 and product is 216.

Given: $P(7, k) = 60 P(7, k-3)$. Then: $k = $

If the $p^{th}$ term of a G.P. is $x$ and the $q^{th}$ term is $y$, then find the $n^{th}$ term:

The sum of the series $0.5+0.55+0.555+\dots$ to $n$ terms is:

The second term of a G.P is $24$ and the fifth term is $81$. The series is

The series $1+10^{-1}+10^{-2}+\dots$ to $\infty$ is

The sum of $m$ terms of the series $1+11+111+\dots$ up to $m$ terms, is equal to:

If $(b+c-a), (c+a-b), (a+b-c)$ are in AP then $a, b, c$ are in:

If the AM and GM of two numbers is $6.5$ and $6$ the no.'s are:

If AM and HM for two numbers are $3$ and $3.2$, respectively. GM will be:

The $n^{th}$ term of the series $3 + 7 + 13 + 21 + 31 + \dots$ is

The numbers $x$, $8$, $y$ are in G.P. and the numbers $x$, $y$, $-8$ are in A.P. The values of $x$ and $y$ respectively shall be

If $a^x = b^y = c^z$ and $a, b, c$ are in G.P., the $x, y, z$ are in

If $a^x = b^y = c^z = e^{1/2}$ then $a, b, c$ are in GP then $x, y, z$ are in

The sum of the first two terms of a GP is $5/3$ and the sum of infinity of the series is 3. The common ratio is

In a GP, if fourth term is $3$ then the product of first seven terms is

In a G. P, sixth term is $729$ and the common ratio is $3$, then the first term of G.P is

In a geometric progression, the second term is $12$ and sixth term is $192$. Find $11^{th}$ term.

If $5^{th}$ term of G.P. is $32$ and $8^{th}$ term of G.P. is $8$ then $6^{th}$ term of G.P. is

Which term of the sequence $2, 4, 8, 16 \dots$ is $2048$?

The $5^{th}$ and $8^{th}$ terms of a GP series is $27$ and $729$. Then find the $10^{th}$ term.

Four Geometric Means between $4$ and $972$ are

The sum up to infinity of the series $S = \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \dots$ is

The $3^{rd}$ term of a G.P is $\frac{2}{3}$ and $6^{th}$ term is $\frac{2}{81}$, then the first term is

Find the sum to infinity of the following series: $1 - 1 + 1 - 1 + \dots \infty$

Find the product of: $(243), (243)^{\frac{1}{6}}, (243)^{\frac{1}{36}}, \dots \infty$

The sum of the first eight terms of a G.P. is five times the sum of the first four terms; then the common ratio is:

For what values of $x$, the number $-\frac{2}{7}, x, -\frac{7}{2}$ are in G.P.?

If $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}$ and $a,b,c$ are in GP then $x, y, z$ are in

If $x, y$ and $z$ are the terms in G.P., then the term $x^2 + y^2, xy + yz, y^2 + z^2$ are in

The sum of the infinite series $1 + \frac{2}{3} + \frac{4}{9} + \dots$ is

In a G.P. If the third term of a GP is $\frac{2}{3}$ and $6^{th}$ term is $\frac{2}{81}$, then the first term is

Sum upto infinity series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^n} + \dots$ is

The sum of first eight terms of geometric progression is five times the sum of the first four terms. The common ratio is

The sum of three numbers in a geometric progression is $28$. When $7$, $2$ and $1$ are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers?

The sum of the first two terms of an infinite geometric series is $15$ and each term is equal to the sum of all the terms following it, then the sum of the series is

Three numbers are in AP and their sum is $21$. If $1, 5, 15$ are added to them respectively, they form a G.P. The numbers are

The sum of three numbers in G.P. is $70$. If the two extremes by multiplied each by $4$ and the mean by $5$, the products are in AP. The numbers are

If $a, b, c$ are in AP and $x, y, z$ are in GP, then the value of $x^{(b-c)} y^{(c-a)} z^{(a-b)}$ is

The sum of the series $1 + 11 + 111 + \dots$ to $n$ terms is

The sum of the following series $4 + 44 + 444 + \dots$ to $n$ terms is:

Find the sum of the series. $243 + 324 + 432 + \dots$ to $n$ terms

Find the sum to $n$ terms of the series: $7+77+777+\dots$ to $n$ terms:

$\sum n^3$ defines:

The $n^{th}$ term of the sequence $-1, 2, -4, 8, \dots$ is

If the sum of $n$ terms of an A.P. is $3n^2-n$ and its common difference is $6$, then its third term is:

The first and last terms of an arithmetic progression are $5$ and $905$. Sum of the terms is $45,955$. The number of terms is

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was $1,500$ after $4$ years of service and $1,800$ after $10$ years of service, what was his starting salary and what is the annual increment in rupees?

A person pays $975$ in monthly installments, each installment is less than former by $5$. The amount of $1^{st}$ installment is $100$. In what time will the entire amount be paid?