Question

write a explicit formula for the following arithmetic sequence 75, 73, 71, 69, 67

Answer 1

The explicit formula for an arithmetic sequence can be written in the form;

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

Where;

$\begin{gathered} a_1=first\text{ term} \\ d=\text{common difference of the arithmetic sequence} \end{gathered}$

for the given arithmetic sequence;

$\begin{gathered} a_1=75 \\ d=73-75 \\ d=-2 \end{gathered}$

Therefore, the explicit formula can be written as;

$\begin{gathered} a_n=75+(n-1)(-2) \\ a_n=75-2(n-1) \\ a_n=75-2n+2 \\ a_n=75+2-2n \\ a_n=77-2n \end{gathered}$

The explicit formula is;

$a_n=77-2n$