Question

For the given A.P : $5,10,15,20\_\_\_$. Find the common difference $(d)$.

Answer 1

Hint: Arithmetic progression is a series or a sequence of numbers in a particular order such that the difference of two consecutive numbers is constant throughout the series. Here the question asks for the common difference, which means we have to subtract two consecutive terms to find the common difference.

Formula used: If three numbers are in an A.P. then the difference of first and second term is the same as the difference of second and third term. This difference is called the common difference of the series and is denoted by the letter $d$. This can mathematically represented as:
$d = b - a = c - b$
Where $a,b,c$ are in an arithmetic progression and $d$ is the common difference.

Complete step-by-step answer:
Arithmetic progression is a series or a sequence of numbers in a particular order such that the difference of two consecutive numbers is constant throughout the series. To understand this better, we look at the most common arithmetic progression that can be explained, the series of natural numbers.
$0,1,2,3,4...$
Here we can see that the difference of the first and second term is the same as the difference of the third and the second term, that is $1$ .
Given in the question is an arithmetic progression $5,10,15,20\_\_\_$ whose common difference we need to find.
We do this by subtracting consecutive terms.
That is,
$d = 10 - 5 = 5$
We confirm this with other terms
$ \Rightarrow d = 15 - 10 = 5$
$ \Rightarrow d = 20 - 15 = 5$

Thus, we can see that the A.P. given in the question has the common difference that is equal to $5$.

Note:
Even though the question already mentioned that the sequence was an A.P., it is important to check by solving the common difference for all consecutive terms and not just one.make sure the errors are reduced while calculation.