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

User Caxapexac
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2 Answers

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Answer: There are six different ways to write 45 as the sum of consecutive natural numbers.

Here is the step-by-step explanation of how we can calculate this:

1. Start by subtracting 1 from 45, so we have 44.

2. Divide 44 by 2 and round down to 22, since we are dealing with natural numbers.

3. 22 is half of our total, so we can subtract this from 45 to get 23.

4. Finally, to figure out how many ways we can write the sum of consecutive natural numbers, we use a formula of n x (n+1)/2, where n is the number of terms in the consecutive numbers.

5. To calculate this, we plug 23 into the formula to get: 23 x 24/2 = 276.

6. This means that there are 6 different ways to write 45 as the sum of consecutive natural numbers: 1 + 2 + 3 + ... + 24; 2 + 3 + 4 + ... + 23; 3 + 4 + 5 + ... + 22; 4 + 5 + 6 + ... + 21; 5 + 6 + 7 + ... + 20; and 6 + 7 + 8 + ... + 19.

User Sam Su
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3 votes

Answer:

Five ways

Explanation:

there are five ways wherein 45 can be written as a sum of consecutive natural numbers

User Ozrix
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