find the sum of all number between 200 and 400 which are divided by 3
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The numbers lying between 200 and 400 which are divisible by 7 are 203,210,217,...399
∴ First term, a=203
Last term, a
n
=399 & Common difference, d=7
Let the number of terms of the A.P. be n.
∴a
n
=399=a+(n−1)d
⇒399=203+(n−1)7
⇒7(n−1)=196
⇒n−1=28⇒n=29
∴S
29
=
2
29
(203+399)
=
2
29
(602)=(29)(301)=8729
Thus, the required sum is 8729
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