Question

 Find the sum of all number between 100 and 300 which are divisible by 7 ?
1. 5586
2. 5454
3. 4455
4. 4544

Answer 1

Correct Answer - Option 1 : 5586

Concept:

For an AP, a1 = First term , an = Last term and d = Common difference

The sum of n terms  = \(\rm \frac n 2 (a_1 + a_n)\)

nth terms of AP = an = a1 + (n - 1)d

 

Calculations:

The first number which is divisible by 7 greater than 100 is =105 & the number which is less than 300 is 294

So, sequence of AP is 105, 112, 119 ,..., 294 having a = 105 , d = 7 and a_n = 294

First we have to find n . 

a_n = a + ( n - 1)d 

⇒ 294 = 105 + (n - 1)7 

⇒ n = 28 

Now S₂₈ = \(\frac{28}{2}\)(105 + 294) = 14 × 399 = 5586