Question

what is the sum of all positive integers lying between 200 and 400 that are multiples of 7

Answer 1

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, ­­­­­­­­… 399

∴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

S=29/2(203+399)=8729

Answer 2

a = 203

d = 7

L = 399

=> a +(n-1) d = 399

=> 203 + (n-1)7 = 399

=> (n-1) 7 = 196

=> n - 1 = 28

=> n = 29

Sn = n/2 [ a + L]

= 29 / 2 [ 203 + 399]

= 29 × 602 / 2

= 29 × 301

= 8729