How many terms of the sequence given below are integers? 21, 7, \frac{21}{5},. . .,\frac{21}{2n-1},n\inN

CAT 2016 Quantitative Ability

Question : 28 of 34

Marks: +1, -0

How many terms of the sequence given below are integers?

21, 7, {21}/{5},. . .,{21}/{2n-1},n∈N

Validate

Solution:

21/{2n-1}

= m(say), where m is an integer.
For m to be an integer, (2n - 1) should be 1,3, 7 or 21 i.e. one of the factors of 21.
Hence, the number of integers in the sequence is 4.

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