Sequence and SeriesMCQMTP Oct 21Question 1848 of 212
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The second term of a G.P is 24\displaystyle 24 and the fifth term is 81\displaystyle 81. The series is

Options

A16,36,24,54,\displaystyle 16, 36, 24, 54, \dots
B24,36,53,\displaystyle 24, 36, 53, \dots
C16,24,36,54,\displaystyle 16, 24, 36, 54, \dots
DNone of these
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Correct Answer

Option c16,24,36,54,\displaystyle 16, 24, 36, 54, \dots

All Options:

  • A16,36,24,54,\displaystyle 16, 36, 24, 54, \dots
  • B24,36,53,\displaystyle 24, 36, 53, \dots
  • C16,24,36,54,\displaystyle 16, 24, 36, 54, \dots
  • DNone of these

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Detailed Solution & Explanation

Let the first term be a\displaystyle a and common ratio be r\displaystyle r.
Given:
t2=ar=24t_2 = ar = 24
t5=ar4=81t_5 = ar^4 = 81
Dividing:
r3=8124=278    r=32r^3 = \frac{81}{24} = \frac{27}{8} \implies r = \frac{3}{2}
Substitute r=32\displaystyle r = \frac{3}{2} back to find a\displaystyle a:
a(32)=24    a=16a\left(\frac{3}{2}\right) = 24 \implies a = 16
The G.P. series is:
16,24,36,54,16, 24, 36, 54, \dots
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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