Question

The second term of an A.P is 2 and the sixth term is - 14. What is he first term and the 9th term?​

Answer 1

Answer: a₁=6 a₉=-26

Explanation:

a₂=2 a₆=-14 a₁=? a₉=?

a₂=a₁+(2-1)d

a₆=a₁+(6-1)d

a₁+d=2 (1)

a₁+5d=-14 (2)

Subtract equation (1) from equation (2):

4d=-16

Divide both parts of the equation by 4:

d=-4

Hence,

a₁+(-4)=2

a₁-4+4=2+4

a₁=6

a₉=a₁+(9-1)d

a₉=6+8(-4)

a₉=6+(-32)

a₉=6-32

a₉=-26

Answer 2

denote by u¹ the first term

hence u⁹ is the 9th term

`u_(n) = u_(1) + (n - 1)d`

`u_(2) = 2 \: \: \: \: \: \: u_(6) = - 14 \\ u_(1) + (2 - 1)d = 2 \\ u_(1) + (6 - 1)d = - 14`

`u_(1) + d = 2 \\ u_(1) + 5d = - 14 \\ \\ \: \: \: (u_(1),d)=(6,-4)`

`u_(9) = u_(1) + (9 - 1)d \\ u_(9) = u_(1) + 8d \\ u_(9) = 6+ (8)( - 4) \: \\ u_(9) = - 26`