The arithmetic mean of the series 1 2 4 8 16…

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The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , 2n is –

  1. A. $$\frac{{{2^n} – 1}}{{n + 1}}$$
  2. B. $$\frac{{{2^n} + 1}}{{n}}$$
  3. C. $$\frac{{{2^n} – 1}}{{n}}$$
  4. D. $$\frac{{{2^{n + 1}} – 1}}{{n + 1}}$$

Answer: Option D

Here is complete explanation of The arithmetic mean of the series 1 2 4 8 16….

Solution(By ExamCraze Team)

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 = $$frac{{{2^{n + 1}} - 1}}{{n + 1}}$$

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