Question

1. the 24th term of the sequence -5, -11, -17, -23, ... is
2. -149
3. -143
4. 133
5. 139

hint: what is the common difference?
plug into the formula: you can use the following formula to find any term in an arithmetic sequence:
$a_n = a_1 + (n - 1) d$
$a_1$ - first term in sequence
$n$ - the position of requested term
$d$ - the common difference

Explanation:

Step1: Identify the first term and common difference

The sequence is \(-5, -11, -17, -23, \dots\). The first term \(a_1 = -5\). To find the common difference \(d\), subtract the first term from the second term: \(d=-11 - (-5)=-11 + 5=-6\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). We need to find the \(24^{\text{th}}\) term, so \(n = 24\), \(a_1=-5\), and \(d=-6\). Substitute these values into the formula:
\[

$$\begin{align*} a_{24}&=-5+(24 - 1)\times(-6)\\ &=-5+23\times(-6)\\ &=-5-138\\ &=-143 \end{align*}$$

\]

Answer:

1. -143