Question

For an A.P if a=6 & S10=195 then show that Sn+3÷

Answer 1

given,
a = 6
S10 = 195

use formula,

Sn = n/2{ 2a + ( n - 1)d }

S10 = 10/2 { 2.6 + (10-1)d }

195 = 5 { 12 + 9d}

39 = 12 + 9d

27 = 9d

d = 3

now ,

S (n+3)/S(n-8) = (n+3)/2 {12 +(n + 3 -1)3}/(n-8)/2 {12 + (n - 8 -1)3 }

= (n+3)(12 + 3n +6)/(n - 8)(3n -15)
=3 (n + 6)(n +3)/5 (n -8)( n -5)