Question

The third term in an arithmetic sequence is 10 and the fifth term is 26.If the first term is a1,which is an equation for the nth of this sequence?

Answer 1

Third Term: 10
 Fifth Term: 26

  10 + x = 26
- 10        - 10
           x = 16
16 ÷ 2 = 8

     First Term: -6
Second Term: 2
    Third Term: 10
  Fourth Term: 18
      Fifth Term: 26

-6, 2, 10, 18, 26
 +8  +8  +8  +8

a(n) = a₁ + d(n - 1)
a(n) = -6 + 8(n - 1)
a(n) = -6 + 8(n) - 8(1)
a(n) = -6 + 8n - 8
a(n) = 8n - 6 - 8
a(n) = 8n - 14

The equation for the nth term of this sequence is 8n - 14.