Question

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

a = {−15, −7, 1, ... }

Answer 1

Consider the following arithmetic sequence:

{-15, -7, 1, …} ...... (1)

 

The first term of given sequence is a1 = -15

 

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

d = a2 – a1

    = -7 – (-15)

   = -7 + 15

   = 8

 

Consider the recursive formula for an arithmetic sequence,

an = an-1 + d, for n ≥ 2 ...... (2)

 

Substitute d = 8 in equation (2), the recursive formula for the nth term of the given arithmetic sequence will be,

an = an-1 + 8, for n ≥ 2

 

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

a1 = -15

 an = an-1 + 8, for ≥ 2.

 an = an-1 + 8, for ≥ 2.