Question

Find the sum of all the integers between 55 and 5555 which are divisible by 7

Answer 1

Sum of all the integers between 55 and 5555 which are divisible by 7 is 22,03,551.

Given:

• Numbers between 55 and 5555.

To find:

• Find the sum of all the integers between 55 and 5555 which are divisible by 7.

Solution:

Formula/Concept to be used :

1. General term of AP: $\bf a_n = a + (n - 1)d$
2. Sum of n terms of AP: $\bf S_n = \frac{n}{2} (a + l)$

here, a: first term

d: common difference

l: last term

Step 1:

Write few numbers which are divisible by 7 lies between 55 and 5555.

56, 63, 70..., 5551

here,

First term of AP (a)=56

common difference (d)=7

Last term (l)=5551

Step 2:

Find total numbers.

Put the values in general term.

$5551 = 56 + 7(n - 1)$

or

$5551 - 56 = 7(n - 1)$

or

$7(n - 1) = 5495$

or

$n - 1 = \frac{5495}{7}$

or

$\bf n = 786$

Step 3:

Find the sum of all numbers.

$S_n = \frac{786}{2} (56 + 5551)$

or

$S_n = 393 \times 5607$

or

$\bf S_n = 22,03,551$

Thus,

Sum of all the integers between 55 and 5555 which are divisible by 7 is 22,03,551.

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Learn more:

1) How many whole numbers each divisible by 7 lies between 200 and 700 ?

https://brainly.in/question/19567315

2) Find the sum of all 3 digit natural multiples of 6.

https://brainly.in/question/5031644

Answer 2

Answer:

2203551

Step-by-step explanation:

To Find:- Sum of all the integers between 55 and 5555 divisible by 7.

Solution:-

The integers divisible by 7 starting from 55 are:

56,63,70,77,.........,5551

∴ This forms an A.P. with first term = 56, common difference = 7

and last term = 5551.

Let the number of terms be n, common difference = d, first term = a.

Now, last term = first term + (n-1)d

⇒ 5551 = 56 + 7n - 7

⇒ 5551 - 49 = 7n

⇒ n = $\frac{5502}{7}$

⇒ n = 786.

Now, Sum = $\frac{n}{2}$ [2a + (n-1) d]

                 = $\frac{786}{2}$ [2 × 56 + (786-1) 7]

                 = 393 [112 + 5495]

                 = 393 × 5607

                 = 2203551

∴ Sum of all the integers between 55 and 5555 divisible by 7 is                          2203551.

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