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The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , 2n is -
Answer & Solution
Correct Answer:
Option
D
The given series is a G.P. with first term, a = 1 and common ratio, r = 2,
It has (n + 1) terms.
∴ Sum of the terms of the series
= $$\frac{{{2^{n + 1}} - 1}}{{2 - 1}}$$
= 2n + 1 $$ - $$ 1
Arithmetic mean = $$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$$
It has (n + 1) terms.
∴ Sum of the terms of the series
= $$\frac{{{2^{n + 1}} - 1}}{{2 - 1}}$$
= 2n + 1 $$ - $$ 1
Arithmetic mean = $$\frac{{{2^{n + 1}} - 1}}{{n + 1}}$$
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