a] Explicit formula
–4, 1, 6, 11, 16
from the given sequence:
the common difference is:
d=1-(-4)=5
this implies that the series is an arithmetic series thus it will take the explicit form
an=a+(n-1)d
where:
a=first term
d=common difference
hence
plugging in the values we obtain the explicit formula for the series is:
an=-4+5(n-1)
simplifying gives us:
an=-4+5n-5
hence
an=5n-9
b] The 100th term
Using the formula for the series, the 100th term will be found as follows:
an=5n-9
n=100
hence
a₁₀₀=5(100)-9
=500-9
=491
