State an explicit rule for the nth term of the recursively-defined sequence.
-$\mathrm { a } _ { \mathrm { n } } = \mathrm { a } _ { \mathrm { n } - 1 } + 8 ; \mathrm { a } _ { 1 } = 1$
A) $a _ { n } = 8 + 1 ( n - 1 )$
B) $a _ { n } = 8 + 1 ( n )$
C) $a _ { n } = 1 + 8 ( n )$
D) $a _ { n } = 1 + 8 ( n - 1 )$

Question

Quizplus · Accepted Answer

The explicit formula for the nth term of the sequence is $a_n = a_1 + 8(n - 1)$, where $a_1 = 1$. This simplifies to $a_n = 1 + 8(n - 1)$, which matches option D. This formula calculates the nth term by adding the initial value (1) to 8 times the number of terms after the first (n-1).

State an Explicit Rule for the Nth Term of the Recursively-Defined