Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
