Question

The sum of five consecutive odd natural number is 165​.what are the numbers

Answer 1

$\boxed{\boxed{\bf{Given:}}}$

The sum of five consecutive odd natural number is 165​.

$\boxed{\boxed{\bf{To\:\:be\:\:found:}}}$

All the five consecutive odd natural numbers whose sum is 165​.

Let one odd number be $\red{\sf{x}}$.

other odd consecutive numbers will be

$\red{\sf{x+2}}$, $\red{\sf{x+4}}$, $\red{\sf{x+6}}$, $\red{\sf{x+8}}$

$\red{\underline{\tt{According\:\:to\:\;the\:\:question-}}}$

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 165

→ 5x + 20 = 165

→ 5x = 165 - 20

→ 5x = 145

→ x = 145 ÷ 5

→ x = 29

So,

The first odd natural number is 29

other numbers are

$\red{\sf{x+2}}$ = 29 + 2 = 31

$\red{\sf{x+4}}$ = 29 + 4 = 33

$\red{\sf{x+6}}$ = 29 + 6 = 35

$\red{\sf{x+8}}$ = 29 + 8 = 37

$\gree{\underline{\sf{Verification-}}}$

29 + 31 + 33 + 35 + 37

= $\red{\sf{(29 + 31)}}$ + $\blue{\sf{(33 + 35)}}$ + 37

= $\red{\sf{60}}$ + $\blue{\sf{68}}$ + 37

= $\green{\sf{(60 + 68)}}$ + 37

= $\green{\sf{128}}$ + 37

= $\boxed{\boxed{\bf{165}}}$

Answer 2

${\underline{\sf{Question}}}$

The sum of five consecutive odd natural number is 165.what are the number

${\underline{\sf{Solution}}}$

Let the first five consecutive odd numbers be x,x+2,x+4,x+6,x+8.

According to the Question:

The sum of five consecutive odd natural number is 165.then ,

x+(x+2)+(x+4)+(x+6)+(x+8)=165

5x+20=165

5x=145

x= 29

Other Number's :

x+2=29+2=31

x+4=29+4=33

x+6=29+6=35

x+8=29+8=37

$\rule{200}2$

Verification:

x+x+2+x+4+x+6+x+8

= 29+31+33+35+37

= 165

Hence , Proved