## In the sequence 14, 18, 22, 26, …, every term is four more than the previous term. How many of the first 100 terms are divisible by

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## Answers ( )

general term for sequence is

10 + 4n where n = 1,2,3,…

4n + 10 = 2(mod 4)

we have to find n for which

4n + 10 = 0 (mod 8)

4n = -10 (mod 8)

4n = 6 ( mod 8)

here gcd of 4n and 8 is atleast 4.

4 does not divide 6

hence, this congruence has no solution

i.e. there is no term in the sequence which will be divisible by 8.