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) $a_n = n + 34$

Explanation:

Step1: Identify common difference

$d = 26 - 30 = -4$

Step2: Use arithmetic sequence formula

La fórmula del término n-ésimo de una sucesión aritmética es $a_n = a_1 + (n-1)d$, donde $a_1=30$.
Sustituimos valores:
$a_n = 30 + (n-1)(-4) = 30 -4n +4 = -4n +34$

Step3: Match with options

La expresión obtenida coincide con la opción B.

Answer:

B) $a_n = -4n + 34$