In an arithmetic sequence, a_(17) = -40 and a_(28) = -73. Explain how to use this information to write a recursive formula for this sequence.

Question

In an arithmetic sequence,
`a_(17)` = -40 and
`a_(28)` = -73. Explain how to use this information to write a recursive formula for this sequence.

Answer 1

The common difference is equal the difference between the given terms divide by the difference between the term numbers:

`d=(a_(28)-a_(17))/(28-17)\to d=(-73-(-40))/(11)=(-33)/(11)=-3`

Calculate the first term:

`a_1=a_(17)-16d\\\\a_1=-40-16(-3)=-40+48=8`

The recursive formula is:

`a_n=\left\{\begin{array}{ccc}a_1=8\\a_(n+1)=a_n-3\end{array}\right`