Sequence and SeriesMCQPYQ Jul 21, MTP Nov 21Question 1797 of 212
All Questions

If the sum of n\displaystyle n terms of an AP is 2n2\displaystyle 2n^2, then 5th\displaystyle 5^{th} term is

Options

A20
B50
C18
D25
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option c18

All Options:

  • A20
  • B50
  • C18
  • D25

Ad

Detailed Solution & Explanation

Given the sum of n\displaystyle n terms is Sn=2n2\displaystyle S_n = 2n^2.
The nth\displaystyle n^{\text{th}} term tn\displaystyle t_n is:
tn=SnSn1=2n22(n1)2=4n2t_n = S_n - S_{n-1} = 2n^2 - 2(n-1)^2 = 4n - 2

Now, find the 5th\displaystyle 5^{\text{th}} term (t5\displaystyle t_5):
t5=4(5)2=18t_5 = 4(5) - 2 = 18
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.

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