Question

Find the series if ${{a}_{n}}=9-5n$.

Answer 1

Hint: We will be using the concept of series and sequence to solve the problem. We will be using the concept of arithmetic progression to solve the problem. We will be substituting different values of n in the equation and find the corresponding series.

Complete step-by-step solution -
Now, we have to find the series if ${{a}_{n}}=9-5n$.
Now, we have the ${{n}^{th}}$term of the series that is ${{a}_{n}}=9-5n$.
So, for the first term we put n = 1. Therefore,
$\begin{align}
  & {{a}_{1}}=9-5\times 1 \\
 & =9-5 \\
 & =4 \\
\end{align}$
Now, for the second term we substitute n = 2.
$\begin{align}
  & {{a}_{2}}=9-5\times 2 \\
 & =9-10 \\
 & =-1 \\
\end{align}$
Now, for the third term we substitute n = 3.
$\begin{align}
  & {{a}_{3}}=9-5\times 3 \\
 & =9-15 \\
 & =-6 \\
\end{align}$
So, the series is of form ${{a}_{1}},{{a}_{2}},{{a}_{3}}......$
Therefore, the series is 4, -1, -6……..

Note: To solve these types of questions it is important to note that we have been given ${{n}^{th}}$ term of a series. So, from using this we can find the any term of the series by substituting the different values of n.