Question

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

Answer 1

Given:

nth term = 5n-2

Let n = 1

$First\; term = {a}_{1} = 5(1)-2 = 3$

Let n = 2

$Second\; term = {a}_{2}=5(2)-2= 8$

Let n = 3

$Third\; term = {a}_{3} = 5(3)-2=13$

To find Common difference:

Common difference = d = ${a}_{3} - {a}_{2} = {a}_{2} - {a}_{1}$

= 13 - 8 = 8 - 3 = 5

To find 19th term:

${a}_{19} = a + (n-1)d$

= 3 + 18(5)

=93

So,

First term $({a}_{1})$= 3

Common difference (d) = 5

19th term $({a}_{19})$ = 93