Question

In a GP the sum of first two terms is -4 and the 5th term is 4 times the 3rd term find the GP

Answer 1

In a gp, if the first term is 'a' and common ratio

is 'r'

Given,

t0+t1=-4

a+ar=-4

a(1+r)=-4. ==>eq 1

Also given,

t5=4(t3)

ar^(5-1)= 4(ar^(3-1))

ar^4=4(ar^2)

r^4=4r^2

r^4-4r^2=0

r^2(r^2-4)=0

r^2(r^2-2^2)=0

r^2(r-2)(r+2)=0

r^2=0 or r-2=0 or r+2=0

so,r= -2,0,2

r=2 since it cannot be negative

so substitute r=2 in eq 1


a(1+2)=-4

a=-4/3

so the required GP is

a,ar,ar^2,ar^3,............

-4/3,(-4/3)*2,(-4/3)*4,...........


Hope it helps you!!!!!