Given the arithmetic sequence with a_{1} is 4, find the 100^{th} term.

a_{1} = 4

We need to get to an explicit rule. That means we need to first locate the first term.

Next, identify the common difference.

{a_{n}} = a_{1} + d(n-1)

Use this information to put together an explicit rule using the general form.

Plug in the term number needed, in this case 100, for n in your formula.

Example 5

Determine how many terms exist in the sequence 1, 6, 11, … 91, 96.

d = 5 a_{1} = 1 a_{n} = 96

Locate the common difference, first term, and last term of the sequence.

a_{n} = a_{1} + d(n-1) 96 = 1 + 5(n-1)

Use the information you've gathered and the general rule of an explicit arithmetic sequence to create an equation with one variable, the number of terms, n.