​ What is the recursive rule for the sequence?

Hello Hev123!

 

The nth term of an arithmetic sequence with the first term A and common difference B, can be expressed as:

 

\(a_n=A+B(n-1)\)

 

The explicit rule given is in simplified form, so we need to find the first term and common difference. 

 

We plug 1 for n, in the given rule, and we get:

 

\(a_1=48-11\cdot1=37\)

 

We know the first term in 37. To find the common difference, we want to find the second term.

 

\(a_2=48-11\cdot2=26\)

 

The common difference is 26 - 37 = -11. 

 

You are correct.

 

I hope this helped,

 

Gavin