Question

Find the number of integers between 100 and 300 which are divisible by 7

Answer 1

Answer:

the last number divisible by 7 between 100 and 300 is 294

Step-by-step explanation:

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Answer 2

we have to find sum of integers between 100 and 300 divisible by 7

Now,

if we see,

the first number between 100 and 300 divisible by 7 is 105

therefore,

next number will be (105+7) i.e. 112

and so on

and the last number divisible by 7 between 100 and 300 is 294.

So, it forms an A.P

105, 112, 119,..............,294

Now,

first term, a = 105

last term, l = 294

and,

common diffrence, d = 7

now,

294 = 105 + 7(n-1)

=> 7(n-1) = 294-105

=> n- 1 = 189/7

=> n = 27+1

=> n = 28

Therefore,

there are 28 terms in thus A.P

Now,

sum of all terms, S = n(a+l)/2

=> S= 28(105+294)/2

=> S = 14 × 399

=> S = 5586

HENCE,

sum of terms = 5586