. Find a G.P. for which the sum of first twoterms is -4 and the fifth

1.	. Find a G.P. for which the sum of first twoterms is -4 and the fifth term is 4 times thethird term.
Answer» let the G.P be. a ,ar, ar² , ar³ , ar⁴ now , sum of first two terms is a+ar = a(1+r) = -4 ....(1) and ar⁴ = 4ar² => r² = 4 ,... so, r = ±2 now putting both the values of r in (1) we get. a(1+2) = -4 so, a = -4/3 or a(1-2) = -4 , a = 4 so, G.P is 4, -8,16,-32,.... or -4/3 , -8/3 , -16/3 , -32/3 ,-64/3

. Find a G.P. for which the sum of first twoterms is -4 and the fifth term is 4 times thethird term.

Answer»

let the G.P be. a ,ar, ar² , ar³ , ar⁴

now , sum of first two terms is a+ar = a(1+r) = -4 ....(1)

and ar⁴ = 4ar² => r² = 4 ,... so, r = ±2

now putting both the values of r in (1)

we get. a(1+2) = -4 so, a = -4/3

or a(1-2) = -4 , a = 4

so, G.P is 4, -8,16,-32,....

or -4/3 , -8/3 , -16/3 , -32/3 ,-64/3