Respuesta :
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.
[tex]\begin{gathered} a_2-a_1=-51-(-36)=-15 \\ a_3-a_1=-66-(-36)=-15 \end{gathered}[/tex]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
[tex]a_n=a+(n-1)d[/tex]a = -36 and d = -15, so
[tex]\begin{gathered} a_n=-36+(n-1)(-15) \\ a_n=-36-15n+15 \end{gathered}[/tex]So
[tex]a_n=-21-15n[/tex]This is the formula for nth term.
Also,
[tex]a_n-a_{n-1}=-15[/tex]This is recursive formula.
Final Answer:
[tex]\begin{gathered} a_n-a_{n-1}=-15 \\ a_n=-21-15n \end{gathered}[/tex]