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The given sequence is 11, 31, 51, 72 The nth term of this sequence can be expressed as an = 11 + (n - 1) × 20 Therefore, the nth term is 11 + (n - 1) × 20, where n is the position of the term in the sequence.
tn = 1.5*n2 - 1.5*n + 1
Assuming this is a linear or arithmetic sequence, the nth term is Un = 31 - 8n. But, there are infinitely many polynomials of order 5 or higher, and many other functions that will fit the above 5 numbers.
1 and 11/20
There are infinitely many possible answers. the simplest polynomial is Un = -n4 + 12n3 - 47n2 + 78n - 41