Question

In how many different ways can the number 45 be written as the sum of consecutive natural numbers?​

Answer 1

There are different five ways in which 45 can be written as the sum of consecutive natural numbers.

• Natural numbers are also called as positive integers (Eg: 1,2,3.... are natural as well as positive with + sign)

Hope it helps!!!

Answer 2

The number 45 can be written in five different ways as the sum of consecutive natural numbers.

Given: The number 45

To Find: Ways in which 45 can be written as the sum of consecutive natural numbers

Solution: To find the consecutive numbers, we will use the following equation:

a + (a + 1) + (a + 2) + (a + 3) + ..... + (a + (k - 1))

By solving this equation we get:

$\frac{k}{2} (2a + (k - 1))$

$\frac{k}{2} (2a + (k - 1))$ = 45

Now, let k = 2:

$\frac{2}{2} (2a + (2 - 1)) = 2a + 1$

2a + 1 = 45

a = 22

a + 1 = 23

Adding two consecutive numbers:

22 + 23 = 45

Now, let k = 3

$\frac{3}{2} (2a + (3 - 1)) = 3a + 3$

3a + 3 = 45

3a = 42

a = 14

Adding three consecutive numbers:

14 + 15 + 16 = 45

Now, let k = 5

$\frac{5}{2} (2a + (5 - 1)) = 5a + 10$

5a + 10 = 45

5a = 35

a = 7

Adding five consecutive numbers:

7 + 8 + 9 + 10 + 11 = 45

Now, let k = 6

$\frac{6}{2} (2a + (6 - 1)) = 6a + 15$

6a + 15 = 45

6a = 30

a = 5

Adding three consecutive numbers:

5 + 6 + 7 + 8 + 9 + 10 = 4

Now, let k = 9

$\frac{9}{2} (2a + (9 - 1)) = 9a + 36$

9a + 36 = 45

9a = 9

a = 1

Adding nine consecutive numbers:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Therefore, the number 45 can be written as the sum of consecutive natural numbers in five different ways.

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