Question

2x is an even number. What is the fifth odd number immediately after it?

Answer 1

Hint: We have been given an even number. And we have to find the fifth odd number after it. To solve this we will apply the formula:
$2n - 1$ , where $n$ shows the ${n^{th}}$ number after $2x$ .
We should know that the odd numbers are in arithmetic progression (A.P):
$1,3,5,7,9,11...$
 And their sum is given by
${S_n} = 1 + 3 + 5 + 7... + (2n - 1)$ .

Complete step-by-step solution:
Let us first understand the definition of even numbers and odd numbers.
Even numbers: We know that any number which is divisible by $2$ is called an even number i.e. if a number when divided by $2$ leaves no remainder , then the number is called an even number. As for example:
$2,4,6,8,42,100,126...$
Odd numbers: The numbers which are not exactly divisible by $2$ are called an odd number i.e. they leave a remainder.
Examples of an odd numbers are:
$1,3,,7,81,99,273...$
So to find an odd number with an even number we add
 $2n - 1$ .
Here we have been given that
$2x$ is an even number.
So an odd number after this will be of the form:
$2x + (2n - 1)$ where $n$ shows the ${n^{th}}$ number after $2x$ .
So let us find the first number first, i.e.
$n = 1$ .
By putting this in the formula we have:
$2x + (2 \times 1 - 1)$
On simplifying this value we have:
$2x + (2 - 1) = 2x + 1$
When we put
$n = 2$, we have:
$2x + (2 \times 2 - 1)$
On simplifying this value we have:
$2x + (4 - 1) = 2x + 3$
For the third number we put
$n = 3$, it gives:
$2x + (2 \times 3 - 1)$
On simplifying this value we have:
$2x + (6 - 1) = 2x + 5$
To find the fourth odd number we put
$n = 4$, we have:
$2x + (2 \times 4 - 1)$
On simplifying this value it gives:
$2x + (8 - 1) = 2x + 7$
Now for finding the fifth odd number, we will put
$n = 5$, so it can be written as:
$2x + (2 \times 5 - 1)$
On simplifying this value we have:
$2x + (10 - 1) = 2x + 9$
Hence the fifth odd number immediately after $2x$ is $2x + 9$ .

Note: We should note that only integers are classified as even or odd numbers. Decimals and fractions cannot be put under this category. We should note that when we add two odd numbers, the answer will be even. As for example:
 $1 + 3 = 4$
There is another property: Odd number $ - $ Odd number $ = $ Even number .
We can see this with example i.e.
 $3 - 1 = 2$
Or,
$17 - 13 = 4$ .