Question

Write a recursive formula to represent the sequence:-36,-51,-66,-81....

Answer 1

Given: Given a sequence -36,-51,-66,-81....

Required: Recursive formula to represent the sequence.

Explanation:

For the given sequence,

Let us check the difference between consecutive terms.

`\begin{gathered} a_2-a_1=-51-(-36)=-15 \\ a_3-a_1=-66-(-36)=-15 \end{gathered}`

Thus, it is clearly an arithematic progression(A.P.) with first term a = -36 and common difference d = -15.

So let us find the nth term of the AP

`a_n=a+(n-1)d`

a = -36 and d = -15, so

`\begin{gathered} a_n=-36+(n-1)(-15) \\ a_n=-36-15n+15 \end{gathered}`

So

`a_n=-21-15n`

This is the formula for nth term.

Also,

`a_n-a_(n-1)=-15`

This is recursive formula.

Final Answer:

`\begin{gathered} a_n-a_(n-1)=-15 \\ a_n=-21-15n \end{gathered}`