Question

Sum of all numbers between 500 to 1000 which are divisible by 2

Answer 1

Answer:

THIS IS A SUM WHICH CAN BE SOLVED THROUGH ARITHMETIC PROGRESSION

the first term divisible by 2 between 500 and 1000 is 500 and last term is 1000

AP SERIES WOULD BE

500,502,504,506.......1000

SO

a = 500

d = 2

Tn = 1000

Tn = a+ (n-1)d

1000 = 500 + (n-1)(2)

1000 = 500 +2n - 2

1000 - 498 = 2n

502 = 2n

n = 251

now for sum

Sn = n/2[a + Tn]

= 251/2 [500 + 1000]

= 188250 ANS

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