Question

i need help like now i only have 15 sec make it as quick as possible.

Answer 1

In general, an arithmetic sequence is given by the following formula

$a_n=a_1+(n-1)d$

Where d is a constant.

In our case, notice that (1,-8)=(1,a_1), and (2,-2)=(2,a_2); thus,

$\begin{gathered} a_1=-8_{} \\ \text{and} \\ a_2=a_1+(2-1)d=a_1+d \\ \Rightarrow a_2=-8+d \\ \text{but} \\ a_2=-2 \\ \Rightarrow-2=-8+d \\ \Rightarrow d=-2+8=6 \\ \Rightarrow d=6 \end{gathered}$

Thus, the explicit formula is

$\begin{gathered} \Rightarrow a_n=-8+6(n-1) \\ \text{with} \\ d=6 \end{gathered}$

The answers are d=6, a_n=-8+6(n-1)