Q. 44.3( 27 Votes )
Find the sum of all numbers between 200 and 400 which are divisible by 7.
The numbers lying between 200 and 400 which are divisible by 7
are as follows: -
203, 210, 217, … 399
Since the common difference between the consecutive terms is constant. Thus, the above sequence is an A.P.
∴First term, a = 203
Last term, l = 399
Common difference, d = 7
Let the number of terms of the A.P. be n.
∴ an = 399 = a + (n –1) d
⇒ 399 = 203 + (n –1) 7
⇒ 7 (n –1) = 196
⇒ n –1 = 28
⇒ n = 29
We know that -
Sum of n terms of an A.P(Sn) = (n/2)[a + l]
S29 = (29/2)[203 + 399]
= 29 × 301
Thus, the required sum is 8729.
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