Sequence and SeriesMCQPYQ Dec. 21Question 1763 of 212
All Questions

The sum of first n\displaystyle n terms an AP is 3n2+5n\displaystyle 3n^2+5n. The series is:

Options

A8,14,20,26,...\displaystyle 8, 14, 20, 26, ...
B8,22,42,68,...\displaystyle 8, 22, 42, 68, ...
C22,68,114,...\displaystyle 22, 68, 114, ...
D8,14,28,44,...\displaystyle 8, 14, 28, 44, ...
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option a8,14,20,26,...\displaystyle 8, 14, 20, 26, ...

All Options:

  • A8,14,20,26,...\displaystyle 8, 14, 20, 26, ...
  • B8,22,42,68,...\displaystyle 8, 22, 42, 68, ...
  • C22,68,114,...\displaystyle 22, 68, 114, ...
  • D8,14,28,44,...\displaystyle 8, 14, 28, 44, ...

Ad

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=S2S1=228=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=S3S2=4222=20t_3 = S_3 - S_2 = 42 - 22 = 20

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

Related Comparison Tables

More Questions from Sequence and Series

Ready to Master Sequence and Series?

Practice all 212 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free