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Find the value of n if it is given that nth term of the A.P. 5, 8, 11, 14, . . . . . . is 68.

Answer
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Hint: Let us consider a variable a which will represent the first term of an arithmetic progression and let us consider a variable d which will represent the common difference of the same arithmetic progression. The ‘nth’ term of this arithmetic progression is given by the formula ${{a}_{n}}=a+\left( n-1 \right)d$. Using this formula, we can solve this question.

Complete step by step solution:
Before proceeding with the question, we must know the formula that will be required to solve this question.
In sequences and series, if we have an arithmetic progression having its first term as a and the common difference as d, then the nth term of this arithmetic progression i.e. ${{a}_{n}}$ is given by the formula,
${{a}_{n}}=a+\left( n-1 \right)d$ . . . . . . . . . . . . (1)
In this question, we are given an A.P. 5, 8, 11, 14, . . . . The first term (a) of this A.P. is 5.
The common difference of this A.P. can be found out by subtracting the first term from the second term and is given by d = 8 – 5 = 3.
Also, it is given in the question that the nth term of this A.P. is 68 and we have to find the value of n. Substituting a = 5, d = 3 and ${{a}_{n}}=68$ in formula (1), we get,
$\begin{align}
  & 68=5+\left( n-1 \right)\left( 3 \right) \\
 & \Rightarrow 3\left( n-1 \right)=63 \\
 & \Rightarrow n-1=21 \\
 & \Rightarrow n=22 \\
\end{align}$
Hence, the value of n = 22.

Note: There is a possibility that one may commit a mistake while calculating the value of d. It is possible that one may subtract the second term from the first term instead of subtracting the first term by the second term to find the common difference which will lead us to an incorrect answer.