We have changed our privacy policy. In addition, we
use cookies on our website for various purposes. By continuing on our website, you consent
to our use of cookies. You can learn about our practices by reading our
privacy policy.

Given the explicit rule: {a_{n}} = 2n – 5, find a_{10}.

a_{10} = 2(10) – 5

Substitute 10 for n in your rule.

a_{10} = 20 – 5a_{10} = 15 Simplify and solve for a_{10}.

Example 2

Find the explicit rule for the sequence: 2, 4, 6, 8, …

a_{1} = 2 a_{2} = 4 a_{3} = 6

Match each term with their term number, n.

1 to 2, 2 to 4, 3 to 6

Look at each term number next to its corresponding term.

1 × 2 = 2, 2 × 2 = 4, 3 × 2 = 6

Find a way to relate the term number to each term along the way.

{a_{n}} = 2n

Rewrite the final rule using braces in terms of n. Braces look like this: { }.

Example 3

Find a_{5} for the sequence: 1, 5, 9, …

1 → 5 by adding 4 5 → 9 by adding 4

The term number we want is pretty close to what we are given. So determine a consistent way to get from one term to another.

9 + 4 = 13 13 + 4 = 17

If the term number you need is small enough, just apply the rule and go for it.

a_{5} = 17

Example 4

Find a_{20} for the sequence 2, 4, 8, …

a_{1} = 2 a_{2} = 4 a_{3} = 8 so a_{n} = 2^{n} The term number here is big. So find a rule that allows you to just plug in the term number you need for n.