Question

Given the sequence write an explict formula and find the 78th term-23 -27 -31 -35

Answer 1

We see that there is a difference of 4 between each number:

`\begin{gathered} -23-4=-27 \\ -27-4=-31 \\ -31-4=-35 \end{gathered}`

and so on. Then, we can propose the following formula:

`a_n=-23-4\cdot n`

For instance, when n=0 we have

`\begin{gathered} a_0=-23+0 \\ a_0=-23 \end{gathered}`

when n=1, we have

`\begin{gathered} a_1=-23-4\cdot1 \\ a_1=-23-4 \\ a_1=-27 \end{gathered}`

when n=2, we have

`\begin{gathered} a_2=-23-4\cdot2 \\ a_2=-23-8 \\ a_2=-31 \end{gathered}`

and so on. Then, in order to compute the 78th term, we must substitute n=78 in our formula. It yields,

`\begin{gathered} a_(78)=-23-4\cdot78 \\ a_(78)=-23-312 \\ a_(78)=-335 \end{gathered}`

and the answer is -335