Question

find sum of multiples of 7 from 100 to 1000

Answer 1

a = 105 , an=994 , d = 7

an=a +(n-1)d

and solve it for n
if u need elaboration just ask for it in comment

and use that n in formula


sn= n/2 (a+an)

Answer 2

Ans.

The sequence of multiples of 7 is
105, 112, ... , 994.

First term (a1) = 105,
2nd term (a2) = 112,
. . . . .
. . . . .
. . . . .
n-th term (an) = 994.

Common difference (d) = 7.

So, n-th term = a1 + (n-1)d
or, 994 = 105 + 7(n-1)
or, 7n = 896
or, n = 128.

Therefore the sum is
= a1 + a2 + a3 + ... + an
= (n/2)(a1 + an)
= 128.(105 + 994)
= 128 × 1099
= 140672.

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