NIFT PG 2020 Question Paper with solutions

Question : 30 of 150

Marks: +1, -0

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 one is increased by 8 and so on. The average of the new number is

Solution:

New average

=\;{n a+2+4+8+16+. . .+2^{n}}/{n}

=\;{n a+2({2^{n}-1}/{2-1})}/{n}=a+2 ⋅ \;{2^{n}-1}/{n}

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