Question

if the second term of G.P is 2 and the sum of n terms is 8 find the 1st term and common ratio

pls give fast with explanation​

Answer 1

let a be the first term and r be the common difference.
Then ar=2
r=
a
2
​

sum of infinity is 8
i.e
1−r
a
​
=8

1−
a
2
​

a
​
=8

a−2
a
2

​
=8

a
2
=8a−16

a
2
−8a+16=0
(a−4)
2
=0
Thus a−4=0
a=4