Question

Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, where a0 = 4.

Answer 1

The closed formula for an = an-1 – n will be found using the formula for arithmetic sequence given by:
an=a+d(n-1)
where
a=first term
d=common difference
n=number of terms
From the formula given:
a=4
d=n
thus the formula will be:
an=a+n(n-1)
an=4+n(n-1)