In a geometric progression the sixth term is 8 times the third term and the sum of the 17th and 8th term is 192.

Determine (i) The common ratio (ii) The first term (iii) The sum of the 5th to 11th terms inclusive

solution: Given that in the geometric series sixth term is 8 times the third term

i.e. t6 =8t3 ….. (1)

And the sum of the 17th and 8th term is 192

i.e. t 17 +t 8 =192 …… (2)

(i)common ratio r=2

(ii) first term a= 192/65664 =0.003

(iii)

Sn= a(1-r^n)/(1-r)

number of terms between 5 to 11 is=7

S7= 0.003(127)=0.381