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

This sequence is infinite because it is never ending, due to the... which tells us that this sequence goes on forever. The pattern in this sequence is 3a(ab)^n-1 and the seventh term is 3a^7b^6.

Answer 2

The correct answer is the seventh term of the sequence is 3
`a^(7)b^(6)` and the sequence is infinite.

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.