Question

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

Answer 1

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