Question

Show york work. Determine the value of the first term and write a recursive definition for the following sequence:
12, 7, 2, -3,-8,

Answer 1

To determine the value of the first term in the sequence, we need to identify the pattern in the given terms:

12 - 5 = 7
7 - 5 = 2
2 - 5 = -3
-3 - 5 = -8

The pattern is subtraction of 5 from the previous term. Therefore, the first term in the sequence is:

12 - 5 = 7

Recursive definition:
a_1 = 7
a_n = a_(n-1) - 5 for n > 1