Question

find the sum of all integers between 100 and 300 which are divisible by 7

Answer 1

Numbers between 100 to 300 that are divisible by 7 are

105, 112, 119, 126….. 294

This is arithmetic progression where common difference is 7, 1st term is 105, last term = 294

Total number of terms = {(last term - 1st term)/ common difference } + 1

={ (294–105)/7 } + 1

= 27 + 1 = 28 terms

Sum of AP = n(1st term + last term)/2

n is number of terms

Sum = 28(105+294)/2

= 14(399)

= 14*(400–1)

= 5600 - 14 = 5586 (Ans)

Answer 2

$\huge\bf\mathscr\pink{Your\: Answer}$

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5586

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step-by-step explanation:

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