Question

find how many natural number are there between 100 and 700 which are divisible by 6

Answer 1

Hi.

Here is your answer----

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The numbers which are divisible by 6 between 100 and 700 are----
{ 102, 108, 114,..................696}

We can see the sequence is in A.P. as each term differs from the succeeding terms by 6.

Thus,
First term(a) = 102
Common difference(d) = 108 - 102
                                     = 6
Last term(l) = 696.

Using the Formula,

 l = a + (n-1)d
 696 = 102 + (n-1)6
6(n-1) = 594
  n -1 = 99
  n = 100

Thus, the number of terms divisible by 6 between 100 and 700 is 100 terms.

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Hope it helps.

Have a nice day.