Find a recursive formula for $s_{n}$ , n $\ge$1, for the sequence 1, 6, 41, 286, 2001, ...
A) $s_{n}=7-s_{n-1}$ with $s_{1}=1$
B) $s_{n}=7 s_{n-1}-1$ with $s_{1}=1$
C) $s_{n}=7-s_{n-1}$ with $s_{1}=7$
D) $s_{n}=7 s_{n-1}-1$ with $s_{1}=7$

Question

Quizplus · Accepted Answer

To find a recursive formula, we look at the pattern of the sequence. From 1 to 6, 6 to 41, 41 to 286, and so on, each term is obtained by multiplying the previous term by 7 and then subtracting 1. This pattern is represented by $s_{n}=7s_{n-1}-1$. The first term given is 1, so $s_{1}=1$.

Find a Recursive Formula For sns_{n}sn​ , N ≥\ge≥ 1, for the Sequence 1, 6, 41, 286, 2001

Find a Recursive Formula For $s_{n}$ , N $\ge$ 1, for the Sequence 1, 6, 41, 286, 2001