The 4th term of a G.P is 100 and the 2nd term is 4. Find (a) The common ratio (b) The value of “a" (c) The 3rd term

Answer 1

In GP n-th term is:

an = a • r ⁿ⁻¹

where

a =a1 = first term

r = common ratio

In this case:

a2 = a • r

a2 = 4

a • r = 4

a4 = a • r ³

a4 = 100

a • r ³ = 100

a4 / a2 = 100 / 4 = a • r ³ / a • r

25 = r²

r² = 25

r = √25

r = ± 5

Two case are possible.

1)

r = - 5

a2 = a • r = 4

a • ( - 5 ) = 4

a = 4 / - 5 = - 4 / 5

2)

r = 5

a2 = a • r = 4

a • 5 = 4

a = 4 / 5