How do you find the formula for #a_n# for the arithmetic sequence #a_1=-4, a_5=16#?

1 Answer
May 8, 2017

Answer:

Set up and solve a system of equations using the definition of the arithmetic sequence. Answer: #a_n=-4+5(n-1)#

Explanation:

We know that from the general formula for arithmetic sequences:
#a_n=a_1+(n-1)d#
where #a_n# is the nth term, #a_1# is the 1st term, #n# is the term number, and #d# is the difference between each term.

So, we write out what we know:
#a_1=-4#
#a_5=16#
Using the general formula for arithmetic sequences, the second equation becomes:
#a_5=a_1+(5-1)d=16#
By substituting #a_1=-4# into the above equation, we get:
#-4+4d=16#
Now, we simply solve for d:
#-1+d=4#
#d=5#

Therefore, the formula for the given arithmetic sequence is:
#a_n=-4+5(n-1)#