Question

The fourth term in an arithmetic sequence is 18 and the seventh term is 39. If the first term is a1 , which is an equation for the nth term of this sequence?

Answer 1

aₙ = 7n - 10

Explanation:

The nth term:
`a_n=a_1+d(n-1)`

So:

a₄ = a₁ + 3d

18 = a₁ + 3d ⇒ 3d = 18 - a₁

a₇ = a₁ + 6d

39 = a₁ + 6d

39 = a₁ + 2(18 - a₁)

39 = a₁ + 36 - 2a₁

39 = 36 - a₁

a₁ = -3

3d = 18 - (-3)

3d = 21

d = 7

So the nth term:

`a_n = -3 + 7(n-1)\\\\a_n=-3 +7n - 7\\\\a_n = 7n - 10`