Question

What is the value of x in the geometric sequence x, 3, — ‚ .A. -27B. -9C. -1D. -3

Answer 1

Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get

`(x)/(3)`

if we do that with the second and third numbers, we get

`\frac{3}{\text{ -}(1)/(3)}=\text{ -}(3\cdot3)/(1\cdot1)=\text{ -9}`

this two numbers should be equal. So we get

`(x)/(3)=\text{ -9}`

if we multiply both sides by 3, we get

`x=3\cdot\text{ -9= -27}`

so option A is the correct option.