Write a variable expression to describe the rule for the sequence. then find the 100th term in the sequence. - 4, 1, 6, 11, 16

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