Answer:
r = 4
Step-by-step explanation:
The general term of the geometric sequence is ⇒ an = a * rⁿ⁻¹
Where a is the first term and r is the common ratio
The second term is 24 ⇒ 24 = a * r²⁻¹ = a r ⇒(1)
The fifth term is 1536 ⇒ 1536 = a * r⁵⁻¹ = a r⁴ = (a r) * r³ ⇒ (2)
By substitution with the value of (a r) from eq.(1) at eq.(2)
So, 1536 = 24 r³
∴ r³ = 1536/24 = 64
∴ r = ∛64 = 4
so, the common ratio r = 4
And the first term = 24/4 = 6
The geometric sequence will be ⇒ an = 6 * 4ⁿ⁻¹
