Question

Find the 19th term of the following A.P.
7, 13, 19, 25,...​

Answer 1

Given ,

The AP is 7 , 13 , 19 , 25 , ...

Here ,

First term (a) = 7

Common difference (d) = 6

We know that , the general formula of an AP is given by

$\star \: \: \sf a_{n} = a + (n - 1)d$

Thus ,

$\Rightarrow \sf a_{19} = 7 + (19 - 1)6 \\ \\\Rightarrow \sf a_{19} =7 + (18) \times 6 \\ \\ \Rightarrow \sf a_{19} =7 +108 \\ \\\Rightarrow \sf a_{19} =115$

$\therefore \bold{ \sf \underline{The \: nineteenth \: term \: of \: an \: AP \: is \: 115}}$

Answer 2

$\rule{200}2$

$\huge\bold{\mathtt{QUESTION}}$

➡ Find the 19th term of the following A.P. → 7, 13, 19, 25, ...

$\rule{200}2$

$\huge\bold{\mathtt{SOLUTION}}$

✳ As we know -

☯ $\sf a_n = a + ( n - 1 ) d$

Where , n = no. of term , a = first term , d = common difference .

Now , ATQ -

Here , n = 19 , a = 7 , d = 13 - 7 = 6 .

↪ $\sf a_{19} = 7 + ( 19 - 1 ) 6$

↪ $\sf a_{19} = 7 + 18 ( 6 )$

↪ $\sf a_{19} = 7 + 108$

↪ $\sf a_{19} = 115$

$\sf \:\:\:\:\:\:\:\:\:\:\:{\underline{\red{{19}^{th}\:term\:=\: 115 }}}$

$\rule{200}2$