CAT 2022 Slot 3 Paper

Question : 57 of 66

Marks: +1, -0

The average of all 3-digit terms in the arithmetic progression $38, 55, 72, ...,$ is

Solution:

General term

=38+(n-1) 17=17 n+21=17(n+1)+4=17 k+4

Each term is in the form of

17 {k}+4

Least 3-digit number in the form of

17 k+4

is at

k=6

, i.e. 106
Highest 3-digit number in the form of

17 k+4

is at

k=58

, i.e. 990

106,123,140, . . . . . . . . . .990

990=106+17(n-1)

{n}=53

\text " Sum "={53}/{2}(106+990)=53 × 548

\text " Average "=53 × {548}/{53}=548

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