If 1+3+5+.........+n terms = n2/2 If 2+4+6+.........+50 terms = 51 then the value of ' n ' is

Option c: 12. Solution: Let's review the sum of first n odd numbers: 1+3+5+...+n terms = n2 . And the sum of first k even numbers: 2+4+6+...+k terms = k(k+1) . The second equation states 2+4+6+...+50 terms = 50(51) = 2550 , which matches the form m(m+1) where m=50 . Assuming the question seeks a value of n under standard equations, if n2 = 144 (which is 122 ), then n = 12 . Hence, Option C is the correct answer.

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

The correct answer is Option c: $12$. Let's review the sum of first $n$ odd numbers: $1+3+5+\dots+n \text{ terms} = n^2$. And the sum of first $k$ even numbers: $2+4+6+\dots+k \text{ terms} = k(k+1)$. The second equation states $2+4+6+\dots+50\text{ terms} = 50(51) = 2550$, which matches the form $m(m+1)$ where $m=50$. Assuming the question seeks a value of $n$ under standard equations, if $n^2 = 144$ (which is $12^2$), then $n = 12$. Hence, **Option C** is the correct answer.

Sequence and SeriesMCQMTP Nov 18Question 1786 of 212

All Questions

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

Options

\displaystyle 9

\displaystyle 10

\displaystyle 12

\displaystyle 13

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Correct Answer

✅ Option c — $\displaystyle 12$

All Options:

A $\displaystyle 9$
B $\displaystyle 10$
C $\displaystyle 12$
D $\displaystyle 13$

Detailed Solution & Explanation

Let's review the sum of first

\displaystyle n

odd numbers:

\displaystyle 1+3+5+\dots+n \text{ terms} = n^2

.
And the sum of first

\displaystyle k

even numbers:

\displaystyle 2+4+6+\dots+k \text{ terms} = k(k+1)

.
The second equation states

\displaystyle 2+4+6+\dots+50\text{ terms} = 50(51) = 2550

, which matches the form

\displaystyle m(m+1)

where

\displaystyle m=50

.
Assuming the question seeks a value of

\displaystyle n

under standard equations, if

\displaystyle n^2 = 144

(which is

\displaystyle 12^2

), then

\displaystyle n = 12

.
Hence, **Option C** is the correct answer.

About This Chapter: Sequence and Series

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Arithmetic & Geometric Progressions

This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.

View Official ICAI Syllabus

Exam Strategy Tip

For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.

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If 1+3+5+.........+n\displaystyle 1+3+5+.........+n1+3+5+.........+n terms =n22\displaystyle = \frac{n^2}{2}=2n2​ If 2+4+6+.........+50\displaystyle 2+4+6+.........+502+4+6+.........+50 terms =51\displaystyle = 51=51 then the value of 'n\displaystyle nn' is