Question

The 3rd term of the A.p is 8 and the 9th term of the A.p is exceeds 3times the term by 2 find the A.p

Answer 1

a+2d=8--------------------(i)
a+8d=2(a+d). both are given in question
a+8d=2a+2d
a=6d
put a=6d in eq.(i)
6d+2d=8
8d=8
d=1
put d=1 in eq.(i)
a+2=8
a=6
hence ap is
6,8,10,12,14,16...................




hope it help you

Answer 2

★ Solution

a3 = 8 = a + 2d .......(1)

a + 8d = 2(a + d) .......(2)

From equation 2.

→ a + 8d = 2a + 2d

→ 2a - a = 8d - 2d

→ a = 6d ......(3)

Put value of a in equation 1.

→ 6d + 2d = 8

→ 8d = 8

→ d = 8/8

→ d = 1

$\Large{\implies{\boxed{\boxed{\sf{d = 1}}}}}$

$\rule{200}{2}$

Put Value of d in equation 3.

→ a = 6(1)

→ a = 6

$\Large{\implies{\boxed{\boxed{\sf{a = 6}}}}}$

$\therefore$ A.P = 6, 7, 8, 9, 10 .....……