Question

this question has two parts. first, answer part a. then, answer part b. part a write an equation for the nth term of the arithmetic sequence. 30, 26, 22, 18, ... a) $a_n = 4n + 64$ b) $a_n = -4n + 34$ c) $a_n = 3n + 24$ d) $a_n = n + 34$ part b graph the first five terms of the sequence. a) image of a graph with 30 and $a_n$ axis

Explanation:

Step1: Identify first term and common difference

First term $a_1=30$, common difference $d=26-30=-4$

Step2: Use arithmetic sequence formula

The formula for the $n$th term of an arithmetic sequence is $a_n = a_1 + (n-1)d$. Substitute values:

$$\begin{align*} a_n &= 30 + (n-1)(-4)\\ &= 30 -4n +4\\ &= -4n +34 \end{align*}$$

Step3: Find first five terms

Calculate terms for $n=1$ to $n=5$:

• $n=1$: $a_1=-4(1)+34=30$
• $n=2$: $a_2=-4(2)+34=26$
• $n=3$: $a_3=-4(3)+34=22$
• $n=4$: $a_4=-4(4)+34=18$
• $n=5$: $a_5=-4(5)+34=14$

These are the points $(1,30), (2,26), (3,22), (4,18), (5,14)$ to graph.

Answer:

Part A: B) $a_n = -4n + 34$
Part B: The first five terms are 30, 26, 22, 18, 14. The graph consists of the discrete points $(1,30)$, $(2,26)$, $(3,22)$, $(4,18)$, $(5,14)$ (plotted as individual points on a coordinate plane with $n$ on the x-axis and $a_n$ on the y-axis).