Question

Find the common ratio. a2 = 7; a4 = 1575

Answer 1

Answer:  15

Step-by-step 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

Answer 2

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 = $\frac{1575}{7}$ = 225 ⇒ r = $\sqrt{225}$ = 15