Question

If the nth term of an AP is (5n- 2), find its first term and common difference. Also find its 19th term​

Answer 1

Answer:

a1=5*1-2

a1=3

a2=5*2-2

a2=8

d=a2-a1

=8-3

d=5

a19=a+18d

=3+18*5

=3+90

=93

Answer 2

$\huge\underline\mathrm{Question-}$

If the nth term of an AP is (5n- 2), find its first term and common difference. Also find its 19th term.

$\huge\underline\mathrm{Answer-}$

First term (a) = 3

Common difference (d) = 5

Nineteenth term ($a_{19}$) = 93

$\huge\underline\mathrm{Explanation-}$

Given :

• nth term = (5n-2)

To find :

• first term (a)
• common difference (d)
• nineteenth term ($a_{19}$)

Solution :

We have to put the value of 'n' in these type of questions.

★ Put n = 1

$a_1$ = 5(1) - 2

$a_1$ = 5 - 2

$\mapsto$ $\red{\sf{a_1\:=3}}$

★ Put n = 2

$a_2$ = 5(2) - 2

$\mapsto$ $a_2$ = 10 - 2

$\mapsto$ $a_2$ = 8

Now, common difference (d) = $a_2\:-\:a_1$

$\mapsto$ d = 8 - 3

$\mapsto$ $\red{\sf{d=5}}$

$\rule{200}1$

Now, we have a = 3 and d = 5, so we can find its Nineteenth term.

$a_{19}$ = a + 18d

$\mapsto$ $a_{19}$ = 3 + 18 (5)

$\mapsto$ $a_{19}$ = 3 + 90

$\mapsto$ $\red{\sf{a_{19}\:=93}}$

$\therefore$ Its nineteenth term is 93.