Average of n numbers is a The first number is increased…

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Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by 8 and so on. The average of the new numbers is –

  1. A. $$a + \frac{{2\left( {{2^n} – 1} \right)}}{n}$$
  2. B. $$a + \frac{{{2^{n + 1}} – 1}}{n}$$
  3. C. $$a + \frac{{{2^{n + 1}}}}{n}$$
  4. D. $$a + 2\frac{{{2^{n – 1}}}}{n}$$

Answer: Option A

Here is complete explanation of Average of n numbers is a The first number is increased….

Solution(By ExamCraze Team)

Series:- a, a + 2, a + 4.....
Sum = na + 2 + 4 + ..... upto n terms
Sum = na + Sn
$${S_n} = frac{{2left( {{2^n} - 1} right)}}{{2 - 1}}$$
Average = $$a + frac{{2left( {{2^n} - 1} right)}}{n}$$

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