What is the pattern 432 434 436 438 the answer is 446?

Answer 1

If you mean the 5th term is 446, then

Possibly

• U{n} = (n⁴ - 10n³ + 35n² - 42n + 1744)/4

Giving U{1..8} = {432, 434, 436, 438, 446, 472, 534, 656}

Or

• U{n} = (-43n⁵ + 648n⁴ - 3685n³ + 9780n² - 11908n + 10392)/12

Giving U{1..8} = {432, 434, 436, 438, 446, 42, -2046, -8374}

If you meant the pattern 434, 434, 436, 438 and what term is 446, then:

The pattern your teacher is most likely wanting is

• U{n} = 430 + 2n

Which means 446 = 430 + 2n → 2n = 16 → n = 8; thus 446 is the 8th term.

However, the first one above also works but makes 446 the 5th term - there are infinitely many polynomials which give {432, 434, 436, 438} as the first 4 terms and then 446 as some term afterwards, for example:

• U{n} = (997n⁵ - 15950n⁴ + 94695n³ - 259150n² + 323048n - 117720)/60

gives U{1..8} = {434, 434, 436, 438, 42, 446, 6438, 28390} with 446 as the 6th term.

• U{n} = (n⁵ - 15n⁴ + 85n³ - 225n² + 334n + 12780)/30

gives U{1..8} = {434, 434, 436, 438, 440, 446, 468, 530} also with 446 as the 6th term.