Questionterms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither. a. $\quad a(1)=7, a(n)=a(n-1)-3$ for $n \geq 2$. b. $\quad b(1)=2, b(n)=2 \cdot b(n-1)-1$ for $n \geq 2$. c. $\quad c(1)=3, c(n)=10 \cdot c(n-1)$ for $n \geq 2$. d. $d(1)=1, d(n)=n \cdot d(n-1)$ for $n \geq 2$.

Studdy Solution
Determine if $d(n)$ is arithmetic or geometric by examining the recursive relation.
Calculate the ratio: $$\frac{d(n)}{d(n-1)} = n$$ The ratio is not constant, and the difference: $$d(n) - d(n-1) = (n-1) \cdot d(n-1)$$ The difference is also not constant. Therefore, sequence d is neither arithmetic nor geometric.
Solution Summary: a. Arithmetic sequence with common difference $-3$. b. Neither arithmetic nor geometric. c. Geometric sequence with common ratio $10$. d. Neither arithmetic nor geometric.