Question

Find the 91st term of the arithmetic sequence 28, 8, -12, ...

Answer 1

Answer:

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

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

where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the common difference between the numbers.  

If we are looking for the 91st term, our n = 91;

our a1 is 28, and

the common difference is -20.  Putting all that together gives us the explicit formula for this sequence:

$a_{91}=28-20(91-1)$ and

$a_{91}=28-20(90)$ and

$a_{91}=28-1800$ so

$a_{91}=-1772$