Question

If for a G.P., s2=8 and S4=80, find its first term and the common ratio.​

Answer 1

Answer:

r=-3

Step-by-step explanation:

Let a be the 1st term and r be the common ratio of a G.P. ,accordingly:-

S2=a.(1-r^2)/(1-r)

8=a.(1+r)(1-r)/(1-r)

8=a(1+r)………………………………(1)

S4=a.(1-r^4)/(1-r)

80=a.(1+r^2)(1+r)………………….(2)

On dividing eqn.(1)by eqn.(2)

8/80= 1/(1+r^2)

1/10= 1/(1+r^2)

1+r^2=10

r^2=9

r=+/-(3)

Put r+3 in eqn.(1). 8=4a. or. a=2

Put r=-3 in eqn.(1). 8=-2a. or. a=-4

a= 2 and. r=+3. or. a=-4. and. r=-3. ,Answer.