Question

Find the sum of integers between 100 and 200 that are divisble by6

Answer 1

Divisible by 6

First number between 100 and 200 divisible by 6  is  = 102 and last number that can divisible by 6 between 100 and 200 is  = 198

So,  First term  = a =  102  , Common difference  = d  = 6  , nth term  =  198 

We know formula of nth term in A.P.  =  Tn =  a + ( n - 1 ) d , So

102 + ( n - 1 ) 6 = 198

( n - 1 ) 6 = 96

n  - 1 = 16

n  = 17 

And we know sum of n terms of A.P. = n2[2a + ( n − 1 )d] , So

Sum of  the integers between 100 and 200 that are divisible by 6  = 172[2 × 102 + (17 − 1 )6] = 172[ 204 + 16 ×6]= 172[ 204 + 96] = 172×300 = 17 × 150 = 2550         
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Answer 2

The solution is given in the image.Sum of nth term is
Sn = (n/2)(a+l) where 'a' is the first term and 'l' is the last term.I hope it helps.