Question

Write a recursive definition in function notation for the sequence.

Answer 1

As you can see, the sequence starts at 3 and increases by 2.5 units each time, so a possible formula for the sequence is:

an = 1/2(5n + 1)

let's verify it:

a1 = 1/2(5*1 + 1) = 1/2(6) = 3

a2 = 1/2(5*2 + 1) = 1/2(11) = 5.5

a3 = 1/2(5*3 + 1) = 1/2(16) = 8

a4 = 1/2(5*4 + 1) = 1/2(21) = 10.5