Question

Find the sum of all multiples of 7 lying between 500and 900

Answer 1

Answer:

the multiples of 7 between 500 and 700 are

504, 511, ..........700

therefore

a=504

l=700

d=7

an = a+(n-1)d

700=504+(n-1)7

700-504=7n-7

196+7=7n

203/7=n

n=29

since we got no of terms now we can find sum of 29 terms

Sn=n/2(2a+(n-1)d)

=29/2(2*504 + (29-1)7)

=29/2(1008+196)

=29/2*1204

=29*602

=17458

so the sum of all multiples of 7 between 500 and 700 is 17458

hope it helps

Answer 2

Answer:

39900

Step-by-step explanation:

first multiple = 504

second = 511

last = 896

A.P = 504,511,.........,896

d = 511-504 = 7

a = 504

as, An = a + (n-1)d

896 = 504+(n-1)7

392 = 7n-7

399 = 7n

so, n = 57

and Sn = n/2[a+An]

S57 = 57/2[504+896]

= 57×1400/2

= 57×700

= 39900 ....ans.