Question

The sum of \[5\] consecutive integers is 265

a) 52, 53, 54, 55, 56
b) 51, 52, 53, 54, 55
c) 53, 54, 55, 56, 57
d) 50, 51, 52, 53, 54

Answer 1

To find the sum of 5 consecutive integers, use the formula: Sum = (n/2)(first term + last term). Substitute the possible values to find the correct option, which is a) 52, 53, 54, 55, 56.

Step-by-step explanation:

To find the sum of 5 consecutive integers, we can use the formula: Sum = (n/2)(first term + last term), where n is the number of terms. In this case, we have 5 terms and the sum is 265. Plugging in the values, we get 265 = (5/2)(first term + last term).

Since the terms are consecutive, the difference between any two terms is always 1. So, we can rewrite the equation as 265 = (5/2)(first term + first term + 4).

Simplifying further, we get 265 = (5/2)(2 · first term + 4).

Now, we can solve the equation by substituting the possible values of the first term:

1. For option a: 265 = (5/2)(2 · 52 + 4) = 265, which is correct.
2. For option b: 265 = (5/2)(2 · 51 + 4) = 257.5, which is incorrect.
3. For option c: 265 = (5/2)(2 · 53 + 4) = 272.5, which is incorrect.
4. For option d: 265 = (5/2)(2 · 50 + 4) = 262.5, which is incorrect.

Therefore, the correct option is a) 52, 53, 54, 55, 56.