Question

Write an equation to find the nth term of each sequence, then find the 24th term (a_24):-1,-4,-7,-10

Answer 1

`\begin{gathered} a_n\text{ = 2 - 3n} \\ a_(24)\text{ = -70} \end{gathered}`

Step-by-step explanation

We want to find an equation that represents the nth terms of each sequence.

From observing the sequence, we see that it is an arithmetic sequence.

The nth term of an arithmetic sequence is generally given as:

`a_{n\text{ }}=\text{ a + (n - 1)d}`

where a = first term (in this case -1)

d = common difference

The common difference, d, can be found by subtracting two consecutive terms.

So, for this sequence:

d = -4 - (-1) = -4 + 1

d = -3

Therefore, the nth term of this sequence is given as:

`\begin{gathered} a_n\text{ = -1 + (n - 1)(-3)} \\ a_n\text{ = -1 - 3n + 3} \\ a_n\text{ = 2 - 3n} \end{gathered}`

That is the equation that represents the nth term of the squence.

To get the 24th term, we make n = 24:

`\begin{gathered} a_(24)\text{ = 2 -3(24)} \\ a_(24)\text{ = 2 - 72} \\ a_(24)\text{ = -70} \end{gathered}`