Question

For the following exercises, write a recursive formula for each arithmetic sequence.

a = {−1, 2, 5, ... }

Answer 1

Consider the following arithmetic sequence:

{-1, 2, 5, …} ...... (1)

 

The first term of given sequence is a1 = -1.

 

Common difference of the sequence will be obtained by subtracting its first term from the second term,

d = a2 – a1

   = 2-(-1)

   = 3

 

Consider the recursive formula for an arithmetic sequence,

an = an-1 + d, for n ≥ 2 ...... (2)

 

Substitute d = 3 in equation (2), the recursive formula for the nth term of the given arithmetic sequence will be,

an = an-1 + 3, for n ≥ 2

 

Therefore, the recursive formula for the above arithmetic sequence is,

a1 = -1

an = an-1 + 3, for n ≥ 2.

an = an-1 + 3, for n ≥ 2

an = an-1 + 3, for n ≥ 2.