Sequence and SeriesMCQPYQ June 19Question 1823 of 212
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In a G.P., if the fourth term is '3' then the product of first seven terms is

Options

A37\displaystyle 3^7
B38\displaystyle 3^8
C39\displaystyle 3^9
D33\displaystyle 3^3
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Correct Answer

✅ Option a — 37\displaystyle 3^7

All Options:

  • A37\displaystyle 3^7
  • B38\displaystyle 3^8
  • C39\displaystyle 3^9
  • D33\displaystyle 3^3

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Detailed Solution & Explanation

Let the first term of the G.P. be a\displaystyle a and the common ratio be r\displaystyle r.
We are given that the fourth term is 3\displaystyle 3 (t4=ar3=3\displaystyle t_4 = ar^3 = 3).
The product of the first seven terms is:
Product=t1⋅t2⋅t3⋅t4⋅t5⋅t6⋅t7\text{Product} = t_1 \cdot t_2 \cdot t_3 \cdot t_4 \cdot t_5 \cdot t_6 \cdot t_7
Product=a⋅ar⋅ar2⋅ar3⋅ar4⋅ar5⋅ar6\text{Product} = a \cdot ar \cdot ar^2 \cdot ar^3 \cdot ar^4 \cdot ar^5 \cdot ar^6
Product=a7r1+2+3+4+5+6=a7r21\text{Product} = a^7 r^{1+2+3+4+5+6} = a^7 r^{21}
Product=(ar3)7\text{Product} = (ar^3)^7
Substitute ar3=3\displaystyle ar^3 = 3:
Product=37\text{Product} = 3^7
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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