Question

How do I find the common difference of the arithmetic sequence 2, 5, 8, 11, .....?

Answer 1

Hint: This question is from the topic of sequences. In this question, we are going to know first how to find the common difference of any arithmetic sequence. After that, we will find the common difference of arithmetic sequence which is given in the question. In this question, we will use the formula of arithmetic sequence that is \[{{a}_{n}}=a+\left( n-1 \right)d\].

Complete step by step solution:
Let us solve this question.
In this question, we have asked to find the difference of arithmetic 2, 5, 8, 11,....
For finding common difference, we will use the formula of arithmetic sequence that is \[{{a}_{n}}=a+\left( n-1 \right)d\], where \[{{a}_{n}}\] is the \[{{\text{n}}^{th}}\] term, a is the first term, n is total number of terms and d is the common difference of the arithmetic sequence.
So, in the arithmetic sequence which is given in the question, we can say that 11 is the last or fourth term, 2 is the first term, total number of terms is 4, and we have to find the value of d of that sequence. So, using the same formula and putting the values, we can write
\[11=2+\left( 4-1 \right)d\]
This can also be written as
\[\Rightarrow 11-2=\left( 3 \right)d\]
The above equation can also be written as
\[\Rightarrow 9=3d\]
The above equation can also be written as
\[\Rightarrow 3=d\]
So, from here we can say the value of d is 3.
Hence, we have found the common difference of arithmetic sequence 2, 5, 8, 11,....
The common difference is 3.

Note: As we can see that this question is from the topic of sequences, so we should have a better knowledge in that topic to solve this type of question easily. We should know how to find the common difference of any arithmetic sequence. Remember the formula of arithmetic sequence for solving this type of question easily. The formula is: \[{{a}_{n}}=a+\left( n-1 \right)d\], where \[{{a}_{n}}\] is \[{{\text{n}}^{th}}\] term, a is the first term, n is the total number of terms, and d is the common difference of arithmetic sequence.