Explicit (Direct) Rule for a Sequence
An explicit rule gives the value of any term directly using its position number n.
Practice This ConceptMain explanation
Teacher explanation
If a sequence has a rule like an = 2n + 1, we can find the 10th term by putting n = 10 without listing all previous terms. This is useful when the question asks for a far-away term such as the 50th term.
Example
For an = 3n + 2, the 5th term is a5 = 3(5) + 2 = 17.
Simple analogy
Direct rule means jump straight to the term.
Common confusion
Students sometimes substitute the term value in place of n, but n represents the position, not the term itself.
Exam tip
Before substituting, write what n means: n = required position number.
Study the explicit (direct) rule for a sequence diagram carefully
Use the labelled diagram to keep explicit (direct) rule for a sequence clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of explicit (direct) rule for a sequence in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on explicit (direct) rule for a sequence.
Revision cue
Revise explicit (direct) rule for a sequence through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of explicit (direct) rule for a sequence in one clean line.
2-mark use
Define explicit (direct) rule for a sequence and add one example or condition.
3-mark use
Explain explicit (direct) rule for a sequence, show the method or example, and mention the common mistake.
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