Question

the sum of the first 3 terms of a G.P is 14. If the first term is 2. Find the possible values of the sum of the first five terms.

Answer 1

Step-by-step explanation:

Let the numbers be a,ar,ar

2

∴Sum=a(1+r+r

2

)=14...(1) Also

a+1,ar+1,4ar

2

−1 are in A.P

⇒a(r

2

−2r+1)=2..(2)

Divide (1) and (2) and simplifying

2r

2

−5r+2=0∴r=2,

2

1

and hence a=2,8

∴ Numbers are 2,4,8 or 8,4,2

The required difference of =6