Write the explicit rule for the arithmetic sequence

a1=27 and an = (an-1) + 4

?

This is the recursive rule.

an=4n+27

an=4n+23

an=23n+4

an=27n+4

Given that:

a1=27, an = (an-1) + 4

the second term will be:

a2=a1+4

a2=27+4=31

The explicit formula for arithmetic sequence is given by:

an=a + (n-1) d

where:

a = first term

d=common difference

n=nth term

from the information given:

a=27

d=31-27=4

thus the explicit formula will be:

an=27 + (n-1) 4

an=27+4n-4

an=23+4n

Answer: an=23+4n