If the fourth and the sixth terms of a geometric progression are 8 and 1/2 respectively, then the first term of this sequence will be;

The first term of the sequence is 512 or -512

Step-by-step explanation:

Geometric Progression

The general term n of a geometric progression of first term a1 and common ratio r is:

We are given:

Applying the equation for n=4:

We have:

Applying the equation for n=6:

We have:

Dividing [2] by [1]:

Operating:

Taking the square root:

There are two possible solutions:

From [1]:

This gives also two possibles solutions for a1:

Thus, the first term of the sequence is 512 or -512