Question

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

Answer 1

the number s are
102, 108, 114 .........696

this is in Arithmetic progression ,so

a = 102
d = 6
Tn = 696
n = ?

Tn = a+(n-1) d

696 = 102+(n-1)6

696-102 = 6n - 6

594 +6 = 6n

600 = 6n

600/6 = n

100 = n

so there are 100 natural numbers between 100 and 700 which are divisible by 6

Answer 2

Hi.

Here is your answer---

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The number which are divisible by 6 between 100 and 700 are---

102, 108, 114,...................696

We can see that the sequence is in A.P. as it differs by 6.
     
Thus, First Term(a) = 102
          Common Difference(d) = 6
          Last term(l)  = 696

Using the Formula,
   
     l = a + (n-1)d
 696 = 102 + (n -1)6
 6(n-1) = 696 - 102
 6(n -1) = 594
  (n - 1) = 594/6
  (n - 1) = 99
  n - 1 = 99
  n = 99 + 1
  n = 100

Thus, there are total of 100 natural numbers which are divisible by 6 between 100 and 700.

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Hope it helps.

Have a nice day.