What is the 50th term in the sequence 12 13 14 15 16?

Answer 1

What value would you like?

U{n} = (5x⁵ - 75x⁴ + 425x³ - 1125x² + 1394x - 336)/24

U{1} = 12

U{2} = 13

U{3} = 14

U{4} = 15

U{5} = 16

U{6} = 42

U{50} = 47,672,161

However, I suspect your teacher wants the much simpler sequence U{n} = n + 11

→ U{50} = 50 + 11 = 61

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This shows the problem with extrapolating data beyond given data - there are infinitely many polynomials which will give the sequence so far but will diverge for values outside the given range.

Answer 2

According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid.

For example, using the function Un = (-7*x5 + 105*x4 - 595*x3 + 1575*x22 - 1798*x + 2160)/120, the

50th term would be -13348127. For ANY other value, you simply need to select the appropriate polynomial.

If you select the simplest rule, Un+1 = Un + 11 then the answer is 61.