Question

Find the common ratio.

a2 = 7; a4 = 1575

Answer 1

common ratio r = 15

The n th term of a geometric sequence is

•
`a_(n)` =
`a_(1)`
`(r)^(n-1)`

where
`a_(1)` is the first term and r the common ratio

`a_(2)` =
`a_(1)`r = 7 → (1)

`a_(4)` =
`a_(1)`r³ = 1575 → (2)

divide (2) by (1)

r² =
`(1575)/(7)` = 225 ⇒ r =
`√(225)` = 15

Answer 2

Answer: 15

Explanation:

a₁ = ___, a₂ = 7, a₃ = ____, a₄ = 1575

a₁(r) = a₂

a₂(r) = a₃

a₃(r) = a₄

To get from a₂ to a₄, you have to multiply by r²

⇒ 7r² = 1575

⇒ r² = 225

⇒ r = 15