Question

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

Answer 1

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

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

Answer 2

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