Question

The formula for any arithmetic sequence is a n = a 1 + d(n - 1), where a n represents the value of the nth term, a 1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the arithmetic sequence -7, -3, 1, 5, ...?
Plz help

Answer 1

 -7, -3, 1, 5, .....    from -7 to -3, is +4, from -3 to 1, is +4.

so, is really just adding 4 to get the next term's value, thus the "common difference" is 4, and notice, the first term is -7.

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ a_1=-7\\ d=4 \end{cases} \\\\\\ a_n=-7+(n-1)4$