The common ratio of a G.P. is 3, and the last term is 486. If the sum of these terms be 728, find the first term.
Given: Common Ratio = 3
Sum of GP = 728
Sum of GP for n terms =
Last term say it be n
∴ Tn = arn - 1
⇒ 486 = a3n - 1
⇒
⇒ 1458 = a.3n …(1)
⇒
⇒
⇒ 1456 = a.3n - a…(2)
Subtracting 1 from 2 we get
⇒ 1458 - 1456 = a.3n - a.3n + a
⇒ a = 2.
∴ The first term is 2.