Question

A geometric sequence has all its terms positive. The first term is 7 and the third term is 28.

a.    Find the common ratio.

b.    Find the sum of the first 14 terms.

Answer 1

a = 7 ;  T2 = ar^2 = 28

a.    7r^2 = 28

r^2 = 4

∴ r = 2

b.    Sn = a(r^n - 1)/(r - 1)

 S14 = 7(2^14 - 1)/(2 - 1)

= 7(2^14 - 1)

= 7 x 16 383

= 114 681