Question

# Find the ${10^{th}}$ term of A.P. 2,7,12,.......

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Hint: Find Common difference and then use formula for nth term of an A.P.

We have been given A.P. : 2,7,12,.......
As we know that A.P. or Arithmetic Progression is a sequence of numbers with a common difference between all consecutive terms.
So, let nth term of A.P. be ${A_n}$
So, the given terms are ${A_1},{A_2},{A_3},.....{A_n}$
$\Rightarrow {A_1} = 2,{A_2} = 7,{A_3} = 12$
Let common difference be $d$
So we can say that,
${A_2} - {A_1} = {A_3} - {A_2} = d$
$\Rightarrow d = 7 - 2 = 5$
Now, as we know that ${a_n} = a + \left( {n - 1} \right)d$
Here $n = 10$ and $a = {A_1} = 2$
$\Rightarrow {A_{10}} = 2 + \left( {10 - 1} \right)5$
$\Rightarrow {A_{10}} = 2 + \left( {9 \times 5} \right)$
$\Rightarrow {A_{10}} = 2 + 45$
$\therefore {A_{10}} = 47$

Note: In these types of questions we firstly find the common difference using any two consecutive terms and then use the formula to find nth term of an A.P. Here we put the values of first term, common difference and n in the equation and get our answer