Question

The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?

Answer 1

To find the fifth number in a sequence of 5 consecutive integers with a sum of 265, you can use the formula for the sum of an arithmetic series. The fifth number is 53.

Step-by-step explanation:

To find the fifth number in a sequence of 5 consecutive integers where the sum is 265, we can use the formula for the sum of an arithmetic series. The formula is: Sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. In this case, we have n = 5, so:

1. 265 = (5/2)(2a + 4d)
2. 265 = 2.5a + 10d
3. a + 4d = 53

Since we are looking for the fifth term, we can use the formula a + (n-1)d = 53 to solve for the fifth number:

1. a + 4d = 53
2. a + 4(a+d) = 53
3. 2a + 4d = 53
4. 2a + 8d = 106
5. 2a + 8d - 2a - 4d = 106 - 53
6. 4d = 53
7. d = 13.25

Substituting the value of d back into the equation a + 4d = 53, we can find the value of a:

1. a + 4(13.25) = 53
2. a + 53 = 53
3. a = 53 - 53
4. a = 0

Therefore, the fifth number in the sequence is a + 4d = 0 + 4(13.25) = 53.

11

Answer 2

5 consecutive intergers means intergers that come one after another (1,2,3 or 56,57,58)

So you know that for 5 of those numbers to add up to 256 they all have to be around 256 / 5.

Find an integer close to that, and start trying different consecutive numbers until you get the 265. Then you'll know the 5th number