Question

this question has two parts. first, answer part a. then, answer part b.
part a
use the given arithmetic sequence to write an equation.
-0.75, -0.5, -0.25, 0, …
a) $a_n = 0.25n - 1$
b) $a_n = 25n - 1$
c) $a_n = 0.25n + 1$
d) $a_n = 25n$
part b
find the 7th term of the sequence.

Explanation:

Step1: Identify $a_1$ and common difference $d$

$a_1 = -0.75$, $d = -0.5 - (-0.75) = 0.25$

Step2: Recall arithmetic sequence formula

The general formula is $a_n = a_1 + (n-1)d$

Step3: Substitute values into formula

$$\begin{align*} a_n &= -0.75 + (n-1)(0.25)\\ &= -0.75 + 0.25n - 0.25\\ &= 0.25n - 1 \end{align*}$$

Step4: Calculate 7th term with $n=7$

$$ a_7 = 0.25(7) - 1 $$

Step5: Compute the final value

$$ a_7 = 1.75 - 1 = 0.75 $$

Answer:

Part A: A) $a_n = 0.25n - 1$
Part B: $0.75$