Question

Which term of the A.P. 2,7,12,17…. Is 137?

Answer 1

We are given an arithmetic sequence and asked to find which term of the sequence will be 137.
So we can find the common difference using the formula $d = {a_2} - {a_1}$ and the value of n can be found by using the formula ${a_n} = a + (n - 1)d$

Complete step by step solution: We are given an arithmetic sequence 2 , 7 , 12 , 17 , ……..
Now we need to find which term of this sequence is 137
That is , for which value of n will ${a_n} = 137$
We can use the formula ${a_n} = a + (n - 1)d$to find the value of n
We can find the common difference of the sequence by $d = {a_2} - {a_1}$
$\Rightarrow d = 7 - 2 = 5$
Here ${a_n} = 137$and d = 5
So ,
$\begin{gathered} \Rightarrow {a_n} = a + (n - 1)d \\\ \Rightarrow 137 = 2 + (n - 1)(5) \\\ \Rightarrow 137 - 2 = (n - 1)(5) \\\ \Rightarrow 135 = (n - 1)(5) \\\ \Rightarrow n - 1 = \frac{{135}}{5} \\\ \Rightarrow n - 1 = 27 \\\ \Rightarrow n = 27 + 1 = 28 \\\ \end{gathered}$

From this, we get that the ${28}^{\text{th}}$ term of the AP is $137$.

Note: There is also another formula to find the value of n
We need to assume that the last term of the sequence to be 137 we can find the value of n bby using this formula
$\begin{gathered} \Rightarrow n = \frac{{l - a}}{d} + 1 \\\ \Rightarrow n = \frac{{137 - 2}}{5} + 1 \\\ \Rightarrow n = \frac{{135}}{5} + 1 \\\ \Rightarrow n = 27 + 1 \\\ \Rightarrow n = 28 \\\ \end{gathered}$
So this is another way to find the value of n.