Sequence and SeriesMCQPYQ Dec. 21Question 1763 of 213
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The sum of first n\displaystyle n terms an AP is $3n^2+5n$. The series is:

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

✅ Option a — $8, 14, 20, 26, ...$

All Options:

  • A$8, 14, 20, 26, ...$
  • B$8, 22, 42, 68, ...$
  • C$22, 68, 114, ...$
  • D$8, 14, 28, 44, ...$

Detailed Solution & Explanation

Given the sum of n\displaystyle n terms is Sn=3n2+5n\displaystyle S_n = 3n^2 + 5n.
We can find the terms of the A.P. as follows:
1) First term (t1\displaystyle t_1):
t1=S1=3(1)2+5(1)=8t_1 = S_1 = 3(1)^2 + 5(1) = 8
2) Second term (t2\displaystyle t_2):
S2=3(2)2+5(2)=12+10=22S_2 = 3(2)^2 + 5(2) = 12 + 10 = 22
t2=S2−S1=22−8=14t_2 = S_2 - S_1 = 22 - 8 = 14
3) Third term (t3\displaystyle t_3):
S3=3(3)2+5(3)=27+15=42S_3 = 3(3)^2 + 5(3) = 27 + 15 = 42
t3=S3−S2=42−22=20t_3 = S_3 - S_2 = 42 - 22 = 20

The series is therefore $8, 14, 20, 26, \dots$, which is an A.P. with common difference $d = 6$.
Hence, **Option A** 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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