Find four consecutive odd numbers which add to 64. Give the numbers smallest to largest

four consecutive odd numbers whose sum is 64 are 13, 15, 17 and 19

Step-by-step explanation:

Given : four consecutive odd numbers which add to 64.

We have to find numbers from smallest to largest.

Consecutive numbers are those number having a difference of one between the terms. example: 2,3,4 are consecutive terms.

Consecutive odd numbers are in the form of (2m + 1), (2m+3), (2m+5), etc

Let first odd number = (2m + 1)

then consecutive 3 odd numbers will be (2m + 3), (2m + 5), (2m + 7)

Given : sum of four consecutive odd numbers is 64.

Mathematically written as,

(2m+1) + (2m + 3) + (2m + 5) + (2m + 7) = 64

Solve for m,

4 (2m) + (1 + 3 + 5 + 7) = 64

8m = 64 - 16

8m = 48

m = 6

Thus, numbers are

(2m + 1) = (2 (6) + 1) = 12 + 1 = 13

(2m + 3) = (2 (6) + 3) = 12 + 3 = 15

(2m + 5) = (2 (6) + 5) = 12 + 5 = 17

(2m + 7) = (2 (6) + 7) = 12 + 7 = 19

Thus, four consecutive odd numbers whose sum is 64 are 13, 15, 17 and 19

Step-by-step explanation:

We know that an odd integer is of the form 2m+1. Therefore, we assume that 2m-3, 2m-1, 2m+1 and 2m+3 are the 4 consecutive odd numbers.

It is given that the sum of four consecutive odd numbers = 64, thus

⇒2m-3+2m-1+2m+1+2m+3=64

⇒8m=64

⇒m=8

Therefore the required consecutive odd numbers are:

2m-3=2 (8) - 3=16-3=13,

2m-1=2 (8) - 1=16-1=15,

2m+1=2 (8) + 1=16+1=17,

2m+3=2 (8) + 3=16+3=19

Thus, 13, 15, 17 and 19 are the required consecutive odd numbers.

Numbers from smallest to largest=13, 15, 17 and 19