Write a rule for the nth term of the arithmetic sequence described below. A5 =
91 and a20 =
1
an=
A25=

an = 115 + (n - 1) (-6)

a25 = - 29

Step-by-step explanation:

We use the definition for the nth term of an arithmetic sequence:

an = a1 + (n - 1) d

a5 = 91 = a1 + (5 - 1) d

91 = a1 + 4 d

a20 = 1 = a1 + (20 - 1) d = a1 + 19 d

1 = a1 + 19 d

now we subtract term by term one expression from the other

90 = 4 d - 19 d

90 = - 15 d

divide both sides by -15 to isolate d

d = 90 / (-15) = -6

Now we can calculate what a1 is using for example:

1 = a1 + 19 d

1 = a1 - 114

add 114 to both sides:

115 = a1

Then our general expression for the sequence is:

an = 115 + (n - 1) (-6)

We can now use it to calculate the value of a25:

a25 = 115 + (24) * (-6) = -29