nth term calculator
nth term of 5, 8, 11, 14
3n + 2
It is a linear sequence.
| Terms | 5 | 8 | 11 | 14 |
|---|---|---|---|---|
| 1st differences | 3 | 3 | 3 |
Working
- The differences are all 3 (3, 3, 3), so it is a linear sequence and the nth term starts 3n.
- The zero term (one step before the first) is 5 − 3 = 2.
- nth term = 3n + 2. Check: n = 1 gives 5 and n = 2 gives 8.
Your result
3n + 2. It is a linear sequence. The next terms are 17, 20, 23.
nth term, step by step
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For a linear sequence the nth term is (difference)n + (zero term): 5, 8, 11, 14 goes up in 3s, so the nth term is 3n + 2.
Questions people ask
How do you find the nth term of a linear sequence?
Find the difference between terms: that number goes in front of n. Then work out what to add by going back one step from the first term. 7, 11, 15 goes up in 4s and the zero term is 3, so the nth term is 4n + 3.
How do you find the nth term of a quadratic sequence?
Find the second differences and halve them to get the number in front of n². Subtract that n² term from each term of the sequence, then find the nth term of the linear sequence left, and add the two parts.
How do you know if a number is in a sequence?
Set the nth term equal to the number and solve for n. It is in the sequence only if n is a positive whole number. For 3n + 2 = 50, n = 16, so 50 is the 16th term.
What is the zero term?
The term that would come before the first one: the first term minus the difference. It is the number you add on in a linear nth term.
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How we work this out
What it does
Type a sequence to find its nth term, linear, quadratic or geometric, with the differences and every step shown.
3 to 12 terms in order; 4 or more to test for a quadratic sequence.
Method
- Linear: the common difference d gives dn; add the zero term (first term − d).
- Quadratic: half the constant second difference gives an²; subtract an² from each term and find the nth term of what is left.
- Geometric: a constant ratio r gives first term × rⁿ⁻¹.