Question

Determine the formula for the nth term of the following sequence: -6, -2, 12, 42, 94, 174, ...

Answer 1

`a_n\text{ = }n^3-n^2\text{ - 6}`Step-by-step explanation:

We need to find the relationshipbetween the terms in th sequence:

1st term = -6

`\begin{gathered} \text{let n = nth term} \\ n\text{ in this case = 1} \\ 1st\text{ }term=1^3-1^2-\text{ 6} \\ 1st\text{ }term=\text{ -6} \end{gathered}`

2nd term = -2

To get this:

`\begin{gathered} w\text{here n= nth term} \\ n\text{ in this case = 2} \\ 2ndterm=2^{3\text{ }}-2^2\text{ - 6} \\ 2nd\text{ term = 8 - 4 - 6 = -2} \end{gathered}`
`\begin{gathered} 3rd\text{ }term=3^3-3^2\text{ - 6 = 27 - 9 - 6 = }12 \\ 4th\text{ }term=4^3-4^2\text{ - 6 = 42} \\ 5thterm=5^3-5^2\text{ - 6 = 94} \\ 6th\text{ }term=6^3-6^2\text{ - 6 = 174} \end{gathered}`
`\begin{gathered} \text{Hence, the formula for the nth term:} \\ a_n\text{ = }n^3-n^2\text{ - 6} \\ \text{where a}_n\text{ = nth term} \end{gathered}`