Please I help with this question...

Which rule will find the nth term of the arithmetic sequence
-58, -65, -72, -86, …?

Question

Please I help with this question...

Which rule will find the nth term of the arithmetic sequence
-58, -65, -72, -86, …?

anonymous · Answer

What's the common difference between terms?

anonymous · Answer

I think its 7 but im not sure

anonymous · Answer

That's right. If $a_1$ is the first term of the sequence, $a_2$ is the second, and so on, up to $a_n$ being the $n$th term, you can write the sequence as
$$a_1=-58\
a_2=-58-7=-65\
a_3=-65-7=-72\
\vdots\
a_n=a_{n-1}-7$$
The trick now is to write $a_{n-1}$ in terms of $a_1$.

anonymous · Answer

$$\begin{cases}a_1=-58\
a_2=-58-7\
a_3=-58-7-7\
a_4=-58-7-7-7\
\vdots\
a_n=-58-7-\cdots-7\end{cases}~~\Rightarrow~~\begin{cases}a_1=-58-0(7)\
a_2=-58-1(7)\
a_3=-58-2(7)\
a_4=-58-3(7)\
\vdots\
a_n=-58-(n-1)(7)\end{cases}$$
See the pattern?

anonymous · Answer

yeah I do thanks for explaining this to me

anonymous · Answer

np