Question

The sum of three odd consecutive numbers is 21.find the number

Answer 1

Answer:

the numbers are consecutive odd numbers, the relationship between the smallest number represented by x and the largest number would be x+ 4, since odd numbers each have a distance of 2 on the number line.

Assuming x represents the smallest number, x + 2 represents the middle number and x + 4 represents the largest number.

(x) + (x + 2) + (x + 4) = 255

3x + 6 = 255

3x = 249

x =

249

3

x = 83.

The smallest number is 83. Therefore the numbers are 83, 85 and 87

Answer 2

Step-by-step explanation:

• Given the sum of three consecutive odd numbers are 21 ✓

Let the three consecutive numbers be

=> q,( q+2), (q+4)

$\bold{the \: sum \: of \: the \: numbers \: = 21} \\ \\ w \: can \: apply \: a \: formula \: to \: find \: the \: AP \: r \: series \: of \: the \: three \:consecutive \: numbers \: \\ \\ = > \red{ \boxed{ \bold{ \sum = \frac{n}{2} (2a + (n - 1) \: d)\: } }}$

So let the AP is

q,(q+2),(q+4).....

$= > a = q \\ = > d = q + </strong><strong>2</strong><strong> - q </strong><strong>=</strong><strong> </strong><strong>2</strong><strong>\\ = > n = 3$

So by applying the formula we can find the first term of the AP

$= > \red{\sum = \frac{n}{2}(2a + (n -1 ) d)} \\ \\ = > \red{21 = \frac{3}{2}(2 \times q + (3 - 1) \times</strong><strong>2</strong><strong>) } \\ \\ = > \red{ 21 = (2q + </strong><strong>4</strong><strong>) \frac{3}{2} } \\ \\ = > \red{ 21 = 3 \times (q + </strong><strong>2</strong><strong>)} \\ \\ = > \red{\frac{21}{3} = q + 1 }\\ \\ = > \red{ q = 7</strong><strong> </strong><strong>-</strong><strong>2</strong><strong>} \\ \\ = > \red{ \bold{ \boxed{ </strong><strong>q</strong><strong>=</strong><strong> </strong><strong> </strong><strong>5</strong><strong>}}}$

So the consecutive numbers are

5, (5+2=7), (5+4=9)

=> 5,7,9