Question

the recursive equation of a sequence is given by $a_n = a_{n - 1} + 7$ for $n \geq 1$. if $a_5 = 43$, what is $a_1$? \\(\bigcirc\\) a. 1 \\(\bigcirc\\) b. 6 \\(\bigcirc\\) c. 8 \\(\bigcirc\\) d. 10 \\(\bigcirc\\) e. 15

Explanation:

Step1: Rewrite recursion for reverse

$a_{n-1} = a_n - 7$

Step2: Find $a_4$ from $a_5$

$a_4 = 43 - 7 = 36$

Step3: Find $a_3$ from $a_4$

$a_3 = 36 - 7 = 29$

Step4: Find $a_2$ from $a_3$

$a_2 = 29 - 7 = 22$

Step5: Find $a_1$ from $a_2$

$a_1 = 22 - 7 = 15$

Answer:

E. 15