Question

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Answer 1

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

are as follows: -

203, 210, 217, … 399

Since the common difference between the consecutive terms is constant. Thus, the above sequence is an A.P.

∴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

We know that -

Sum of n terms of an A.P(Sn) = (n/2)[a + l]

S29 = (29/2)[203 + 399]

= (29/2)[602]

= 29 × 301

= 8729

Thus, the required sum is 8729.

JAI SHREE KRISHNA

Answer 2

Answer:

The numbers lying between 200 and 400 which are divisible by 7 are 203,210,217,...399

∴ First term, a=203

Last term, an =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

∴S29 =29/2 (203+399)

= 29/2 (602)=(29)(301)=8729

• Thus, the required sum is 8729