Question

If the 2nd and 5th terms of a

G.P are 6 and 48 respectively,
find the sum of the first four
terms​

Answer 1

45

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)

`(ar^4)/(ar)` =
`(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