Question

first term of an a.p is 6 and the common difference is 5 and find general term

Answer 1

first term of an AP , a = 6

common difference , d = 5

we know, general sequance of arithmetic progression is ; a , a + d, a + 2d, a + 3d....

so, A.P is ; 6, (6 + 5), (6 + 2 × 5), (6 + 3 × 5), .....

⇒AP is ; 6, 11, 16, 21, .....

general term, $a_n$ = a + (n - 1)d

= 6 + (n - 1)5

= 6 + 5n - 5

= 5n + 1

so, general term of given AP is (5n + 1), where n = 1, 2, 3, 4, 5, .....

you can verify it,

first term , $a_1$= 5 × 1 + 1 = 6

2nd term , $a_2$ = 5 × 2 + 1 = 11

3rd term , $a_3$ = 5 × 3 + 1 = 16

fourth term, $a_4$ = 5 × 4 + 1 = 21

............

hence, AP is ; 6, 11, 16, 21....