Question

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

-82, -75, -68, -61, -54, ...
based on this information, create an equation that can be used to find the ( n^{\text{th}} ) term of the sequence, ( a_n ). then, use the equation to find ( a_{20} ).
equation: ( a_n = square )
( a_{20} = square )

Explanation:

Step1: Identify sequence type (Arithmetic)

Check differences: $-75 - (-82) = 7$, $-68 - (-75) = 7$, etc. Common difference $d = 7$.

Step2: Arithmetic sequence formula

Arithmetic sequence formula: $a_n = a_1 + (n - 1)d$. Here, $a_1 = -82$, $d = 7$.
Substitute: $a_n = -82 + (n - 1) \times 7$.
Simplify: $a_n = -82 + 7n - 7 = 7n - 89$.

Step3: Find $a_{20}$

Substitute $n = 20$ into $a_n = 7n - 89$:
$a_{20} = 7(20) - 89 = 140 - 89 = 51$.

Answer:

Equation: $a_n = 7n - 89$
$a_{20} = 51$