The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.
- 8/5
- 8/3
-
72/25
- 56/9
The correct answer is: C
Explanation
Let the common ratio be r so that the first term is 2r.
Sum, s = \(\frac{a}{1-r}\)
ie. 8 = \(\frac{2r}{1-r}\)
8(1-r) = 2r,
8 - 8r = 2r
8 = 2r + 8r
8 = 10r
r = \(\frac{4}{5}\).
where common ratio (r) = \(\frac{second term(n_2)}{first term(a)}\),
r = \(\frac{n_2}{2r}\)
r = \(\frac{4}{5}\) and a = 2r or \(\frac{8}{5}\)
\(\frac{4}{5}\) * \(\frac{8}{5}\) = n\(_2\)
\(\frac{32}{25}\) = n\(_2\)
The sum of the first two terms = a + n\(_2\)
= \(\frac{8}{5}\) + \(\frac{32}{25}\)
= \(\frac{40 + 32}{25}\)
= \(\frac{72}{25}\)