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
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