The $5^{th}$ and $8^{th}$ terms of a GP series is $27$ and $729$. Then find the $10^{th}$ term.

The correct answer is Option d: $6561$. MTP Jun 23

Sequence and SeriesMTP Jun 23Question 1858 of 142

The $\displaystyle 5^{th}$ and $\displaystyle 8^{th}$ terms of a GP series is $\displaystyle 27$ and $\displaystyle 729$ . Then find the $\displaystyle 10^{th}$ term.

Options

\displaystyle 729

\displaystyle 243

\displaystyle 81683

\displaystyle 6561

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Correct Answer

✅ Option d — $\displaystyle 6561$

All Options:

A $\displaystyle 729$
B $\displaystyle 243$
C $\displaystyle 81683$
D $\displaystyle 6561$

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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The 5th\displaystyle 5^{th}5th and 8th\displaystyle 8^{th}8th terms of a GP series is 27\displaystyle 2727 and 729\displaystyle 729729. Then find the 10th\displaystyle 10^{th}10th term.