Practice!

Sample Problem

Find a formula for the arithmetic sequence an given that a5=54 and a10=89.

Solution

An, the arithmetic sequence always has the form an=a1+d(n-1) where d is the common difference and a1 is the first term.

Plug in the information given to us in the problem to form a system of equations

a5=54=a1+d(5-1)=a1+4d

54=a1+4d

a10=89=a1+d(10-1)=a1+9d

89=a1+9d

Subtract the two equations to obtain

5d=35

d=7

By back substituting d=7 into either of the two equations, we can find a1

a1+4(7)=54

a1=54-28=26

an=a1+d(n-1)

an=26+7(n-1)=26+7n-7=19+7n