Question

In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the seventh term. 3a, 3a2b, 3a3b2, 3a4b3. . .

Answer 1

Answer:

The correct answer is the seventh term of the sequence is 3$a^{7}b^{6}$ and the sequence is infinite.

Step-by-step explanation:

The sequence discussed here is infinite. Here there is no bound on the value of n therefore making it an infinite sequence.

The nth term of the sequence is given by $t_{n+1}$ = 3$a^{n+1}b^{n}$, where n is greater than equal to 0.

The sequence would look like this:

3$a^{1}b^{0}$ , 3$a^{2}b^{1}$ , 3 $a^{3}b^{2}$ , 3$a^{4}b^{3}$, 3$a^{5}b^{4}$, 3$a^{6}b^{5}$, 3$a^{7}b^{6}$...

The seventh term of the sequence is given by 3$a^{7}b^{6}$.

This sequence is infinite.