Question

the sum of the average of three consecutive odd number and three consecutive even numbers is 21 .if the highest even no is 16 ,what is the lowest odd number?​

Answer 1

Step-by-step explanation:

Let the three consecutive odd number be (2x + 1),(2x + 3),(2x + 5) and three consecutive even number be 2y,(2y + 2),(2y + 4).

∴Height even number is (2y + 4)

Given that,

2y + 4 = 16

⇒2y = 12

∴ Three consecutive even number is 12,14, and 16.

∴Sum of the three consecutive even number is = 42.

∴Average of the three consecutive even number is = 42/3

=14

Sum of the three consecutive odd number is =2x + 1 + 2x + 3 + 2x + 5

=6x + 9

∴ Average =(6x + 9)/3

=(2x + 3)

∵ The sum of the average of three consecutive odd number and three consecutive even numbers is 21

∴ 14 + 2x + 3 = 21

⇒2x = 21 - 17

⇒2x = 4

∴ Lowest odd number is = (2x + 1) = 4+1=5

∴ Lowest odd number is 5

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Answer 2

Answer:

the lowest odd no.is 5

Step-by-step explanation:

let a be the odd no. then the 3 consecutive odd no. are a, a+2, a+4

let b be the even no. then the 3 consecutive odd no. are b, b+2, b+4

It is given that : b+4=16

$\frac{a+a+2+a+4}{3}$  + $\frac{b+b+2+b+4}{3}$ = 21

$\frac{3a+6}{3}$  + $\frac{3b+6}{3}$ =21

$\frac{3(a+2)}{3}$  + $\frac{3(b+2)}{3}$ =21

a+2 +b+2 =21

a+b+4=21

a+16 =21

a=21-16

a=5