Question

-5, -1, 3...
b. is 119 a term in this sequence? why or why not.

Explanation:

Step1: Identify sequence type & params

The sequence is arithmetic: $a_1=-5$, common difference $d=8$ (since $-5 + 8 = 3$, $3 + 8 = 11$, etc.). The nth term formula is $a_n = a_1 + (n-1)d$.

Step2: Substitute target value

Set $a_n=119$, substitute known values:
$119 = -5 + (n-1) \times 8$

Step3: Solve for n

First, add 5 to both sides:
$119 + 5 = (n-1) \times 8$
$124 = 8(n-1)$
Divide both sides by 8:
$n-1 = \frac{124}{8} = 15.5$
Solve for n:
$n = 15.5 + 1 = 16.5$

Answer:

119 is not a term in this sequence. The position $n$ of a term in a sequence must be a positive integer, but solving for $n$ gives $16.5$, which is not an integer.