Even or odd expressions
Is 6n + 1 always odd, for every whole number n? Try a few values first.
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Step 1 of 3
- n = 4. 2n is 8 dots, in 4 pairs.
- Take one dot away for 2n − 1.
- 2n has no spare, so it is even. 2n − 1 has one, so it is odd.
The rule
Yes: 6n is even, so 6n + 1 is odd.
Parity means odd or even. The nth number in a list is the one at place n. The number in front of n is the one that multiplies n. The plain number is the one with no n beside it.
The nth even number is 2n. The nth odd number is 2n − 1. With an even number in front of n, the plain number decides. With an odd one, the value can be even or odd.
| Expression | In front of n | Plain number | Value |
|---|---|---|---|
| 6n + 1 | 6, even | 1, odd | Always odd |
| 4n + 6 | 4, even | 6, even | Always even |
| 3n + 1 | 3, odd | 1, odd | Even or odd |
Take 3n + 1. For n = 1, 3 × 1 + 1 = 4, which is even. For n = 2, 3 × 2 + 1 = 7, which is odd.
The 40th odd number is 2 × 40 − 1 = 79.