QUESTION

# The general term of a series is given by ${{a}_{n}}=4n-3$. Find the terms ${{a}_{17}}$ and ${{a}_{24}}$ of the series.

Hint: We have been given the question that the general formula of a series is ${{a}_{n}}=4n-3$. So, we can find ${{a}_{17}}$ and ${{a}_{24}}$ by directly substituting the value of n as 17 and 24 in the general equation.

It is given in the question that the general formula of a series is ${{a}_{n}}=4n-3$ and we have to find the value of ${{a}_{17}}$ and ${{a}_{24}}$. So, we can directly find the value of the given terms, ${{a}_{17}}$ and ${{a}_{24}}$ by substituting the value of n as 17 in the first case and n as 24 in the second case in the general equation.
Now, it is given in the question that the general term of a series, ${{a}_{n}}=4n-3$.
Let us consider the first case where we have to find the value of ${{a}_{17}}$, so we get that n = 17. So, we can write it as:
${{a}_{17}}=4\times 7-3$
${{a}_{17}}=68-3=65$
Hence, we get ${{a}_{17}}=65$.
Now, let us consider the second case where we have to find the value of ${{a}_{24}}$, so we get that n = 24. So, we can write it as:
${{a}_{24}}=4\times 24-3$
${{a}_{24}}=96-3=93$
Hence, we get ${{a}_{24}}=93$.
Therefore we get the ${{17}^{th}}$ term of the series as 65 and the ${{24}^{th}}$ term of the series as 93.
Note: In this question, we are given the general term of series so it is easy to find any term of that series, but if the general term of the series is not given in the question, then we have to find the general term of the series first. For example, consider the series 2, 4, 6, 8, 10. The general term of this series can be represented as ${{a}_{n}}=a+(n-1)d$ as this series is in A.P because the common difference of the series is 2. So, the general term can be written as ${{a}_{n}}=a+(n-1)2$. Now we can find any term of the series by substituting the values for n.