Part 02 · Algebra basics · Card 8 of 8
nth term of a sequence
A rule that gives any term in a number pattern from its position n.
Last updated
Analogy
Like a recipe that tells you the 100th item without listing the first 99.
Example
5, 8, 11, 14, ...
Difference is +3, so start with 3n3n gives 3, 6, 9, 12Add 2 to match: 3n + 210th term: 3 x 10 + 2 = 32
In practice
A taxi that adds a flat 2 pound fee and 3 pounds per mile follows 3n + 2.
Practice
Flashcards
- What is the nth term of 5, 8, 11, 14?3n + 2. The terms go up by 3 each time.
Interview questions
- Find the nth term of 2, 9, 16, 23, and use it to find the 20th term.
- The common difference is 7
- So the rule starts with 7n
- 7n - 5 matches the first term 2
- 20th term is 7 x 20 - 5 = 135
Questions people ask
How do you find the nth term of a linear sequence?
Find the common difference between terms. That is the number in front of n. Then compare the sequence with that times table and work out what to add or subtract. For 5, 8, 11, 14, the difference is 3 and the rule is 3n + 2.
How do you check if a number is in a sequence?
Put it equal to the nth term and solve for n. If n comes out as a whole number, the number is in the sequence. For 3n + 2 = 50, n = 16, so 50 is the 16th term. A fraction means it is not.