Answer:
Recursive formula is: [tex]a_1=-1 ; \ \ a_n=a_{n-1}+7[/tex]
Explicit formula is: [tex]a_n=7n-8[/tex]
Step-by-step explanation:
We need to find recursive formula and explicit formula for arithmetic sequence -1,6,13,20,27
In the given sequence First term a₁= -1
Common difference d = 7
Finding Recursive Formula
The recursive formula is of type:[tex]a_1= First \ term[/tex] and [tex]a_n=a_{n-1}+d[/tex]
Since the First term a₁ is -1 and common difference d is 7 so, the recursive formula for given arithmetic sequence will be:
[tex]a_1=-1 ; \ \ a_n=a_{n-1}+7[/tex]
Finding Explicit Formula
The explicit formula is of type: [tex]a_n=a_1+(n-1)d[/tex]
We have
First term a₁= -1
Common difference d = 7
So, explicit formula will be:
[tex]a_n=-1+(n-1)7\\a_n=-1+7n-7\\a_n=7n-8[/tex]
So, explicit formula is: [tex]a_n=7n-8[/tex]
