Sequence and SeriesMCQPYQ July 21Question 1762 of 212
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If the sum of 'n\displaystyle n' terms of an AP (Arithmetic Progression) is 2n2\displaystyle 2n^2, the fifth term is ____.

Options

A20\displaystyle 20
B50\displaystyle 50
C18\displaystyle 18
D25\displaystyle 25
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Correct Answer

Option c18\displaystyle 18

All Options:

  • A20\displaystyle 20
  • B50\displaystyle 50
  • C18\displaystyle 18
  • D25\displaystyle 25

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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 given by:
tn=SnSn1t_n = S_n - S_{n-1}
Substitute Sn\displaystyle S_n and Sn1\displaystyle S_{n-1}:
tn=2n22(n1)2t_n = 2n^2 - 2(n-1)^2
tn=2n22(n22n+1)t_n = 2n^2 - 2(n^2 - 2n + 1)
tn=2n22n2+4n2t_n = 2n^2 - 2n^2 + 4n - 2
tn=4n2t_n = 4n - 2

To find the fifth term (t5\displaystyle t_5):
t5=4(5)2=202=18t_5 = 4(5) - 2 = 20 - 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.

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