Question

Average of the number from 100 to 400 which are divisble by 13

Answer 1

104 to 390 are divisible by 13

Answer 2

➡HERE IS YOUR ANSWER⬇

Ans.

The first number and the last number divisible by 13 between 100 and 400 are 104 and 390 respectively.

Let us consider a AP series :

104 + 117 + 130 + ... + 390

First term = 104

and

Last term = 390

We are having common difference as 13, since the numbers are divisible by 13.

So, Common Difference = 13

We apply the formula for last term of a AP sequence :

Last term = First term + {(n-1l)×Common Difference}, where n is the number of terms in the series.

=> 390 = 104 + {(n-1)×13}

=> (n-1)×13 = 286

=> n - 1 = 22

=> n = 23

Therefore, there are 23 terms in the AP series.

Then the sum of the numbers (between 100 and 400), divisible by 13 is

= (Numbers of terms/2)×(First term + Last term)

= (23/2)×(104 + 390)

= 5681.

♧♧♧ FORMULA GUIDE ♧♧♧

Let, a and l are first and last term of any AP series containing n terms, and d is the common difference.

Then,

1. Last term (l) = a + (n-1)d

2. Sum of the series (S)

= (n/2)×(a + l)

= (n/2)×{2a + (n-1)d}


⬆HOPE THIS HELPS YOU⬅