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
common ratio r = 15
The n th term of a geometric sequence is
• [tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]
where [tex]a_{1}[/tex] is the first term and r the common ratio
[tex]a_{2}[/tex] = [tex]a_{1}[/tex]r = 7 → (1)
[tex]a_{4}[/tex] = [tex]a_{1}[/tex]r³ = 1575 → (2)
divide (2) by (1)
r² = [tex]\frac{1575}{7}[/tex] = 225 ⇒ r = [tex]\sqrt{225}[/tex] = 15
