Question

In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?

Answer 1

r = 8

Explanation:

the nth term of a geometric sequence is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

given a₁ = 3 and a₃ = 192 , then

a₁ = 3 → (1)

a₁r² = 192 → (2)

divide (2) by (1) on both sides

`(a_(1)r^2 )/(a_(1) )` =
`(192)/(3)` ( cancel a₁ on numerator/ denominator of left side ), then

r² = 64 ( take square root of both sides )

r =
`√(64)` = 8