Given:
Sum of GP = 39 + 13√3
Where, a =√3, r = 3/√3 = √3, n = ?
By using the formula,
Sum of GP for n terms = a(rn – 1 )/(r – 1)
39 + 13√3 = √3 (√3n – 1)/ (√3 – 1)
(39 + 13√3) (√3 – 1) = √3 (√3n – 1)
Let us simplify we get,
39√3 – 39 + 13(3) – 13√3 = √3 (√3n – 1)
39√3 – 39 + 39 – 13√3 = √3 (√3n – 1)
39√3 – 39 + 39 – 13√3 = √3n+1 – √3
26√3 + √3 = √3n+1
27√3 = √3n+1
√36 √3 = √3n+1
6+1 = n + 1
7 = n + 1
7 – 1 = n
6 = n
∴ 6 terms are required to make a sum of 39 + 13√3