The common ratio, r, in a geometric sequence whose second term is
24 and whose fifth term is 1536

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

do it yourself this is easy

step-by-step explanation: