Chapter 8.1, Problem 50E

To determine

To check : First two terms of a geometric sequence are positive, then all its terms are positive.

Answer to Problem 50E

True.

Explanation of Solution

Given information :

The first two terms of a geometric sequence are positive.

If the first two terms of a geometric sequence are positive, then the common ratio is also positive. As, the quotient of two positive numbers is also positive.

Also, the third term can be found by multiplying the second term by the common ratio of the sequence.

This implies all the terms of a geometric sequence are positive.

Hence, first two terms of a geometric sequence are positive, then all its terms are positive.