Sequence and SeriesMCQPYQ Nov. 19Question 1757 of 213
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If 2+6+10+14+.........+x=882\displaystyle 2+6+10+14+.........+x=882 then the value of x\displaystyle x is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $82$

All Options:

  • A$78$
  • B$80$
  • C$82$
  • D$86$

Detailed Solution & Explanation

The given series is 2+6+10+14+⋯+x=882\displaystyle 2 + 6 + 10 + 14 + \dots + x = 882.
This is an Arithmetic Progression (A.P.) where:
First term a=2\displaystyle a = 2
Common difference d=6−2=4\displaystyle d = 6 - 2 = 4
Sum of n\displaystyle n terms Sn=882\displaystyle S_n = 882.

Using the sum formula for an A.P.:
Sn=n2[2a+(n−1)d]S_n = n2\displaystyle \frac{n}{2} [2a + (n-1)d]
Substitute the values:
882=n2[2(2)+(n−1)4]882 = n2\displaystyle \frac{n}{2} [2(2) + (n-1)4]
882=n2[4+4n−4]882 = n2\displaystyle \frac{n}{2} [4 + 4n - 4]
882=2n2882 = 2n^2
n2=441  ⟹  n=21n^2 = 441 \implies n = 21

The last term x\displaystyle x is the $21^{st\displaystyle \text{st}}term(\displaystyle term (t_{21}$):
x=a+(n−1)dx = a + (n-1)d
x=2+(21−1)4x = 2 + (21-1)4
x=2+80=82x = 2 + 80 = 82
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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