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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
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a + 2n-1 - 1 n -
a + 2 2n-1 - 1 n -
a + 2n-1 n -
a + 2n - 1 n
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Correct Option: B
Sum of new numbers = na + (2 + 4 + 8 + 16 ..... to n terms)
Now, S = 2 + 4 + 8 + 16 + ..... upto n terms
| Here, a = first term = 2 , r = common ratio = | = 2 | |
| 2 |
It is a geometric series.
| ∴ S = | = | ||
| r - 1 | 2 - 1 |
S = 2 (2n –1)
| ∴ Required average = | |
| n |
| Required average = a + | |
| n |
