Question

The sum of the average of three consecutive odd numbers and three consecutive even numbers is 21. if the highest even number is 16, what is the lowest odd number

Answer 1

let the first even no. = 2x
then
2nd even no. =2x+2
3rd even no. = 2x+4

Given highest even no.=16
so
2x+4=16
2x=12
x=6
so Ist even no.= 2×6 =12
2nd even no.= 14
3rd even no. = 16
average of sum of even no = (12 + 14 + 16)/3
= 42/3
= 14

let 1st odd no. = 2p+1
then
2nd odd no. = 2p+3
3rd odd no. = 2p+5
average sum of odd no. = (2p+1 + 2p+3 + 2p+5)/3
=(6p+9)/3
=2p+3

A.T.Q.
avg sum of even no. + avg sum of odd no. =21
14 + 2p+3=21
2p + 17= 21
2p = 4
p =2

so smallest odd no is 2p +1
i.e.
2×2 +1
=5

Answer 2

The lowest odd number = 5

To find:

the lowest odd number = ?

Given data:

The sum of the average of three consecutive odd numbers and three consecutive even numbers = 21

the highest even number = 16

Formula:

$m=\frac{\text { sum of the terms }}{\text { number of terms }}$

Solution:

let three consecutive odd numbers = p, p+2, p+4

and three consecutive even numbers = p, p+2, p+4

$=\frac{\text { p + p + 2 + p + 4 + p + p + 2 + p + 4 }}{\text { 6 }}$

we know the highest even number = 16

then, other lowest even number is p + 4 = 16

                                                              p = 16 - 4

                                                                 = 12

and middle even number p + 2 = 14

                             12 + 14 + 16 = 42 ÷ 3

                                                = 14

total average - average of even number = average of odd number

21 - 14 = 7

thus the average of odd number = 7

sum of the three consecutive odd numbers = average of odd number x 3

7 X 3 = 21

we know that three consecutive even numbers = p, p+2, p+4, then

p + p + 2 + p + 4 = 21

3P + 6 = 21

3P = 21 - 6

3P = 15

lowest odd number P = 5

middle odd number p + 2 = 7

highest odd number p + 4 = 9

To solve more:

1. The sum of seven numbers is 497 . What is their average?

https://brainly.in/question/5394282

2. If the average of five numbers is -20

and the sum of three of the number is

32 then what is average of the

other two number.​

https://brainly.in/question/10900409