How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?

Natural numbers between 23 and 100 are 24, 25, ...99.

Natural numbers between 23 and 100 which are divisible by 6 are

24, 30, ...96.

In above A.P. first term a = 24, common difference (d) = 6

T(n) = a + (n-1)d

96 = 24 +(n-1) 6

(96-24)/6 + 1 = n

n = 13

Hence such numbers are 13.

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