Main home here.

- The enumeration $0,2,4,8,\cdots$ represents $\cdots$?

- What is the $n$th term of the sequence $2,6,18,54,\cdots$?

- What is the $n$th term of the sequence $-2,-5,-8,-11,\cdots$?

- How many terms are in the sequence $2,-1,-4,-7,\cdots,-46$?

- The third and seventh terms of an arithmetic sequence are $7$ and $27$, respectively. What is the first term?

- The third and fifth terms of a geometric sequence are $18$ and $162$, respectively. Find possible value(s) of the common ratio.

- The three-term sequence $1,(x+1),(x^2+2x+1)$ is geometric. Identify a possible restriction on $x$.

- Find the number of terms in the sequence $-2,1,-\frac{1}{2},\frac{1}{4},\cdots,-\frac{1}{32}$

- A sequence defined recursively by $T_1=2, T_{n}=T_{n-1}-2$ is likely to be $\cdots$?

- The even numbers $2,4,6,8,\cdots$ form