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

Missing number = 8 in the recursive formula

Explanation:

The explicit formula for an arithmetic sequence is
`a_(n)=a+(n-1)d`

Here a = first term of the sequence

n = nth term

d = common difference

Explicit formula for an arithmetic sequence is given in the question

`a_(n)=3 + (n -1)8`

So the first term of the sequence is a = 3

and common difference d = 8

Now the recursive formula of the same sequence will be

`a_(n)-a_(n-1)=d`

`a_(n)=a_(n-1)+d`

Since d = 8 for the sequence.

`a_(n)=a_(n-1)+8`

Therefore the missing number is 8 in the recursive formula.

Answer 2

From the explicit formula:
a=3
an=3+(n-1)8
an=3+8n-8
an=8n-5
thus:
a2=11, a3=19
Thus the sequence
3,11,19...
thus the recursive formula will be:
an=a(n-1)+8
a1=3
Thus the missing value is: 8