Question

find the sum of all integers between 100 and 400 which are divisible by 7

Answer 1

according to me is use the formula sn is equal to n/2 into [2 +(n-1)d]

Answer 2

Answer:

The sum of all integers between 100 and 400 which are divisible by 7 is 10836.

Concept:

Arithmetic Progression (AP)

Given:

Integers between 100 and 400.

Find:

Sum of all integers divisible by 7 in between 100 and 400.

Solution:

First of all we will form an A.P. for the question given.

The first integer divisible by 7 after 100 is 105, then the next integer is given by (105 + 7) = 112.

Similarly, we get the AP as

105, 112, 119, 126, ------------------------, 399.

From the above AP, we have

First term, a = 105

Last term, l = 399

Common difference, d = Second term - First term

                                      = 112 - 105 = 7

First, we will find number of terms.

As we know, Last term or l is given by

$l = a_n = a + (n - 1)d$

$399 = 105 + (n - 1)7\\399 - 105 = 7(n - 1)\\294 = 7(n - 1)\\294/7 = n - 1\\n - 1 = 42\\n = 42 + 1\\n = 43$

Sum of all integers divisible by 7, S = n/2[a + l]

S = 43/2[105 + 399]

S = $\frac{43}{2} \times 504$

S = 43 × 252

S = 10836

Hence,  the sum of all integers between 100 and 400 which are divisible by 7 is 10836.

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