Question

How do you write an equation for the nth term of the arithmetic sequence: 7, 16, 25, 34, ...?

Answer 1

Hint: This question is from the topic of sequence and series. In this question, we will find the nth term of the given arithmetic sequence. In solving this question, we will first find the first term from the given arithmetic sequence. After that, we will find the common difference from the given arithmetic sequence. After that, we will see the formula for nth of the arithmetic sequence. After using that formula, we will find our answer.

Complete step-by-step solution:
Let us solve this question.
In this question, we have asked to find the nth term of the given arithmetic sequence. The given , arithmetic sequence is 7, 16, 25, 34,.....
The first term of the arithmetic sequence is 7.
Now, let us check the common difference. It is found out by finding the difference between the following term and preceding term.
So, we can write the common difference as
\[d=16-7=25-16=34-25=9\]
Hence, we get that the common difference is 9.
Now, let us know about the formula of nth term:
\[{{a}_{n}}=a+\left( n-1 \right)d\], where
\[{{a}_{n}}\]= nth term of the sequence
\[a\]= First term of the sequence
\[d\]= common difference
\[n\]= number of terms
So, using this formula, we can write the nth term of the arithmetic sequence 7, 16, 25, 34, ... as
\[{{a}_{n}}=7+\left( n-1 \right)9\]
The above can also be written as
\[\Rightarrow {{a}_{n}}=7+9n-9\]
The above can also be written as
\[\Rightarrow {{a}_{n}}=9n-2\]
Hence, we get that the nth term of the arithmetic sequence 7, 16, 25, 34, ... is \[\left( 9n-2 \right)\], where n is the number of terms.

Note: We should have a better knowledge in the topic of sequence and series to solve this type of question easily. We should know the following formulas to solve this type of question:
\[{{n}^{th}}\] term of the arithmetic sequence: \[{{a}_{n}}=a+\left( n-1 \right)d\]
Sum of n terms of arithmetic sequence: \[{{S}_{n}}=\dfrac{n}{2}\left( 2a+\left( n-1 \right)d \right)\]
Where,
\[a\] is the first term of the arithmetic sequence
\[d\] is the common difference
\[n\] is the number of terms