Question

Find the \[{n^{th}}\] term of the $A.P.$’s:
$2,7,12,17..........$

Answer 1

Hint: Here we will be using ${t_n} = a + (n - 1)d$ where $a$ is the first term and $d$is the common difference, where $d = $ difference of two consecutive terms. Use this to find the $nth$ term of the $A.P.$.

Complete step-by-step answer:
According to the question , $A.P.$ (Arithmetic Progression series ) i.e. is given :
$2,7,12,17.....$
$a = 2,a + d = 7,a + 2d = 12....$
Where, the first term $(a) = 2$
 The common difference $(d)$
$
   \Rightarrow a + d = 7 \\
   \Rightarrow 2 + d = 7 \\
   \Rightarrow d = 5 \\
$
Hence , we know that the ${n}^{th}$ term of $A.P.$ i.e.
${t_n} = a + (n - 1)d $
Now, substituting the value in the above formula we get,
$\therefore {t_n} = 2 + (n - 1)5$
          $
   = 2 + 5n - 5 \\
   = 5n - 3 \\
 $
Hence , the ${n^{th}}$ term of the series $2,7,12,17....$ is $(5n - 3)$.

Note: Such type of questions require the right use of formula and each term. So, it is advisable to remember such basic formulas while involving into such types of problems of arithmetic progression.