Sequence and SeriesMCQPYQ Nov. 20Question 1828 of 212
All Questions

Three numbers in G.P. with their sum 130 and their product 27,000 are:

Options

A10, 30, 90
B90, 30, 10
CBoth (a) & (b)
D10, 20, 30
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — Both (a) & (b)

All Options:

  • A10, 30, 90
  • B90, 30, 10
  • CBoth (a) & (b)
  • D10, 20, 30

Ad

Detailed Solution & Explanation

Let the three numbers in G.P. be ar,a,ar\displaystyle \frac{a}{r}, a, ar.
Their product is 27,000\displaystyle 27,000:
ar⋅a⋅ar=a3=27000  ⟹  a=30\frac{a}{r} \cdot a \cdot ar = a^3 = 27000 \implies a = 30

Their sum is 130\displaystyle 130:
30r+30+30r=130  ⟹  30(1r+r)=100\frac{30}{r} + 30 + 30r = 130 \implies 30\left(\frac{1}{r} + r\right) = 100
1+r2r=103  ⟹  3r2−10r+3=0\frac{1+r^2}{r} = \frac{10}{3} \implies 3r^2 - 10r + 3 = 0
Factorizing:
(3r−1)(r−3)=0  ⟹  r=3 or r=13(3r-1)(r-3) = 0 \implies r = 3 \text{ or } r = \frac{1}{3}

If r=3\displaystyle r = 3, the numbers are 10,30,90\displaystyle 10, 30, 90.
If r=13\displaystyle r = \frac{1}{3}, the numbers are 90,30,10\displaystyle 90, 30, 10.
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

Void vs Voidable Contract: CA Foundation Law DistinctionAP vs GP: Sequences and Series for CA Foundation Maths

More Questions from Sequence and Series

Sum of progression (a+b)\displaystyle (a+b), (a−b)\displaystyle (a-b), (a−3b)...n\displaystyle (a-3b)...n term is

Find the sum of first twenty-five terms of A.P. series whose nth\displaystyle n^{th} term is (n+25)\displaystyle \left(n+\frac{2}{5}\right)

The first and fifth term of an A.P. of 40\displaystyle 40 terms are −29\displaystyle -29 and −15\displaystyle -15 respectively. Find the sum of all positive terms of this A.P

If the common difference of an AP equals to the first term, then the ratio of its mth\displaystyle m^{th} term and nth\displaystyle n^{th} term is:

Find the value of 1+2+3+...+105\displaystyle 1+2+3+...+105

The first and last terms of an arithmetic progression are 5\displaystyle 5 and 905\displaystyle 905. Sum of the terms is 45,955\displaystyle 45,955. The number of terms is

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