Question

Find the $15^{th}$ term of the A.P.: 2, 5, 8........

Answer 1

Hint: To get any term of the AP series first find the first term of the series and common difference, then find the particular term.

Formula used:
The nth term of the AP series is given by
\[{{a}_{n}} = a+\left( n-1 \right)d\] …… (1)
 where a is the first term and d is the common difference.

Complete step by step answer:
 The given AP series is 2, 5, 8........
Here the first term is 2. Therefore, \[a=2\].
The common difference is calculated as the difference of the succeeding term to the preceding term.
Therefore, common difference is \[5-2=3\]
Thus, \[d=3\]
Now, to get the 15th term substitute \[n=15\] in equation (1) and solve:
\[\begin{align}
  & {{a}_{15}}=a+\left( 15-1 \right)d \\
 & {{a}_{15}}=a+14d \\
\end{align}\]
Substitute the value of a and d in above equation and solve:
\[\begin{align}
  & {{a}_{15}}=2+14\left( 3 \right) \\
 & {{a}_{15}}=2+42 \\
 & {{a}_{15}}=44 \\
\end{align}\]

Hence, the 15 term of the given AP is 44.

Note: While calculating terms in AP always multiply one less than the number of terms with the common difference to get the desired term.