Question

1. a sequence that continues indefinitely is called ______.
2. a sequence that has a limited number of terms is called ______.
3. the sum of the terms in a sequence is called ______.
4. in a ______ sequence, the formula for the nth term is $a_n = a_1 \times r^{(n - 1)}$.

Explanation:

1. The formula $a_n = a_1 \times r^{(n-1)}$ is the standard formula for the nth term of a geometric sequence.
2. The sum of all terms in any sequence is defined as a series.
3. A sequence with a finite, limited number of terms is classified as finite.
4. A sequence that continues without end (infinitely) is classified as infinite.

Answer:

1. geometric
2. series
3. finite sequence
4. infinite sequence