Question

If the 2nd and 5th terms of a

Answer 1

Answer:

45

Step-by-step explanation:

The n th term of a GP is

$a_{n}$ = a$r^{n-1}$

where a is the first term and r the common ratio

Given a₂ = 6 and a₅ = 48, then

ar = 6 → (1)

a$r^{4}$ = 48 → (2)

Divide (2) by (1)

$\frac{ar^4}{ar}$ = $\frac{48}{6}$ , that is

r³ = 8 ( take the cube root of both sides )

r = $\sqrt[3]{8}$ = 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