Question

find the sum of all multiples of 7 lying between 300 and 700

Answer 1

Here a series will be formed as 301, 308, 315, ...........700
So we have the first term a = 301 and d = 7 and last term l = 700
700 = 301+(n-1)7
399 = 7n-7
406=7n
n = 58

Sum = n/2(a+l)
Sum = 58/2(301+700)
= 29 x 1001
= 29029

Answer 2

The no.s lying between 300 & 700 which are divisible by 7 are : 301, 308, 315...........700

first term(a)= 301
last term (l) =700              (an = l= 700)
common difference(d) = 7

Let the no. of term of an A.P be n

an = a+(n-1)d

700 = 301 + (n-1) ×7

(700-301) / 7= n-1

399/7 = n-1

57= n-1

57+1 =n

n=58

Sn= n/2(a=+l)

S58= 58/2 (301+700)

S58 = 29 × 1001

S58 = 29029
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The sum of all multiples of 7 lying between 300 and 700= 29029
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Hope this will help you....