In a geometric progression, that $3^{rd}$ and $6^{th}$ terms are respectively 1 and $-1/8$. The term $(a)$ and common ratio are respectively.

The correct answer is Option d: 4 and $\frac{1}{2}$. PYQ Jan. 21

Sequence and SeriesPYQ Jan. 21Question 1829 of 142

In a geometric progression, that $\displaystyle 3^{rd}$ and $\displaystyle 6^{th}$ terms are respectively 1 and $\displaystyle -1/8$ . The term $\displaystyle (a)$ and common ratio are respectively.

Options

A4 and

\displaystyle \frac{1}{2}

B4 and

\displaystyle -\frac{1}{2}

C4 and

\displaystyle -\frac{1}{2}

D4 and

\displaystyle \frac{1}{2}

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Correct Answer

✅ Option d — 4 and $\displaystyle \frac{1}{2}$

All Options:

A4 and $\displaystyle \frac{1}{2}$
B4 and $\displaystyle -\frac{1}{2}$
C4 and $\displaystyle -\frac{1}{2}$
D4 and $\displaystyle \frac{1}{2}$

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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In a geometric progression, that 3rd\displaystyle 3^{rd}3rd and 6th\displaystyle 6^{th}6th terms are respectively 1 and −1/8\displaystyle -1/8−1/8. The term (a)\displaystyle (a)(a) and common ratio are respectively.