Question

A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n - 1)(8) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula?

Answer 1

As per the given data An= 3+(n-1)8

So to find the value for A(n-1)
We,substitute the the value of n by n-1
Reason,
As An maps from An yo A(n-1)

Therefore 
n will map from n to n-1

Now substituting in the main equation to find value for A(n-1)
A(n-1)=3+(n-1-1)8
           =3+(n-2)8
Now to find the value for ____
We have to find the relation between An and A(n-1)
Let the _____ value be x

An=A(n-1)+x
3+(n-1)8= 3+ (n-2)8  + x

Sovling the equation  we get x=8
So the value is 8

Answer 2

Tn = 3 + 8(n-1)
Tn-1 = 3 + 8(n-2)
Tn - Tn-1 = [3 + 8(n-1)] - [3 + 8(n-2)] = 3+8n-8-3-8n+16 = 8
Tn - Tn-1 = 8 → Tn = Tn-1 + 8