Question

1. the first five terms of a sequence are shown below.

17.9, -5.1, -28.1, -51.1, -74.1, ...
based on this information, create an equation that can be used to find the nth term of the sequence, ( a_n ). then, use the equation to find ( a_{11} ).
equation: ( a_n = )
( a_{11} = )

Explanation:

Step1: Identify sequence type (Arithmetic)

Check common difference: $-5.1 - 17.9 = -23$, $-28.1 - (-5.1) = -23$, so $d = -23$.

Step2: Arithmetic sequence formula

Arithmetic sequence formula: $a_n = a_1 + (n - 1)d$. Here, $a_1 = 17.9$, $d = -23$.
Substitute: $a_n = 17.9 + (n - 1)(-23)$
Simplify: $a_n = 17.9 - 23n + 23 = 40.9 - 23n$

Step3: Find $a_{11}$

Substitute $n = 11$ into $a_n = 40.9 - 23n$:
$a_{11} = 40.9 - 23(11)$
$a_{11} = 40.9 - 253 = -212.1$

Answer:

Equation: $a_n = 40.9 - 23n$
$a_{11} = -212.1$