Question

Assertion (A): The nth term of a G.P. is given by $$T_{n} = ar^{n - 1}$$. 

Reason (R): A sequence $$a_{1}, a_{2}, a_{3} ....$$ is said to a G.P. if $$\frac{a_{1}}{a_{2}} = \frac{a_{2}}{a_{3}} = \frac{a_{3}}{a_{4}} ....$$ = constant known as the common ratio.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is true, but R is false.

Explanation:

The assertion is true: the general term of a G.P. is $$T_n = ar^{n - 1}$$. The reason is false because the common ratio is $$\frac{a_2}{a_1} = \frac{a_3}{a_2} = \cdots = r$$, while $$\frac{a_1}{a_2}, \frac{a_2}{a_3}, \cdots$$ are its reciprocals, not the common ratio.