Find the first term of an arithmetic sequence if

Question

a₅=11 and a₉=19

Answer 1

Use the explicit formula for an arithmetic sequence:

a_n = a₁ + (n-1)d      Let a_n = 19 and a₁ = 11

19 = 11 + (5-1)d

8 = 4d

d = 2

Start at the 5th term (11) and keep subtracting 2 until you are at the first term. 

11-2 = 9

9 - 2 = 7

7 - 2 = 5

5 - 2 = 3 - the first term