Question

If 16, X + 2, 1 are the first three terms of a

geometric sequence, find all possible values
of x.

Answer 1

Answer: x = 2 or x = -6

Explanation:

16, x + 2, 1

Notice that a₁ to a₃ is 2 ratios.

16 · r² = 1

r² = 1/16

r = ± 1/4

If r = 1/4, then a₂ = 16/4

= 4

4 = x + 2 → x = 2

If r = - 1/4, then a₂ = 16/-4

= -4

-4 = x + 2 → x = -6

Answer 2

X=2 or X=-6

Explanation:

The common ratio is either 1/4 or -1/4. Since if we divide 16 by 4 we get 4 and we divide that by 4 get 1 or if we divide 16 by -4 we get -4 and that by -4 to get 1.

A more detailed math explanation:

ar^2/a=1/16

r^2=1/16

r=1/4 or -1/4

This means the second term is either 16(1/4)=4 or 16(-1/4)=-4.

So,

X+2=4 or X+2=-4

Subtract 2 on both sides:

X=4-2 or X=-4-2

X=2 or X=-6