Question

how many numbers between 20 and 200 are exactly divisible by 7 ? find the sum.

Answer 1

Method of Solution :


Number between 20 and 200 are exactly divisible by 7 are 21, 28,35 ....... 196


Here, First term of AP = 21

It's Common Difference = 7


Applying Tn Formula!


Tn = a + (n-1)d

Tn = 21 + (n-1)7

Tn = 21 + 7n - 7


196 = 14 + 7n

196 - 14 = 7n


182 = 7n

•°• n = 26


Now, According to the Question's Statement!

Statement : Sum of Numbers between 20 and 200 are exactly divisible by 7


Using Summation Formula !


Sn = n/2(a+l)

Sn = 26/2(21+196)


Sn = 13 ( 217 )

Sn = 2821


Hence, Required Sum of integers between 20 and 200 are exactly divisible by 7 is $\bf{\huge{28,21}}$