What is the missing number of this pattern 7 16 8 27 9?

Answer 1

The answer will depend on where, in the sequence, the missing number is meant to be. Also, in each case, there are infinitely many possible answers since it is possible to find a polynomial of degree 5 (or higher) that will go through each of the above numbers and ANY other number, missing from ANY position.

Using polynomials of order 4, though, there is only one answer for each position. For example,

First number missing: 171

Un= (-27n4+ 422n3- 2364n2+ 5611n - 4668)/6

Last number missing: 218

Un= (-27n4+ 314n3- 1260n2+ 2041n - 1026)/6

The answer will depend on where, in the sequence, the missing number is meant to be. Also, in each case, there are infinitely many possible answers since it is possible to find a polynomial of degree 5 (or higher) that will go through each of the above numbers and ANY other number, missing from ANY position.

Using polynomials of order 4, though, there is only one answer for each position. For example,

First number missing: 171

Un= (-27n4+ 422n3- 2364n2+ 5611n - 4668)/6

Last number missing: 218

Un= (-27n4+ 314n3- 1260n2+ 2041n - 1026)/6

The answer will depend on where, in the sequence, the missing number is meant to be. Also, in each case, there are infinitely many possible answers since it is possible to find a polynomial of degree 5 (or higher) that will go through each of the above numbers and ANY other number, missing from ANY position.

Using polynomials of order 4, though, there is only one answer for each position. For example,

First number missing: 171

Un= (-27n4+ 422n3- 2364n2+ 5611n - 4668)/6

Last number missing: 218

Un= (-27n4+ 314n3- 1260n2+ 2041n - 1026)/6

The answer will depend on where, in the sequence, the missing number is meant to be. Also, in each case, there are infinitely many possible answers since it is possible to find a polynomial of degree 5 (or higher) that will go through each of the above numbers and ANY other number, missing from ANY position.

Using polynomials of order 4, though, there is only one answer for each position. For example,

First number missing: 171

Un= (-27n4+ 422n3- 2364n2+ 5611n - 4668)/6

Last number missing: 218

Un= (-27n4+ 314n3- 1260n2+ 2041n - 1026)/6

Answer 2

The answer will depend on where, in the sequence, the missing number is meant to be. Also, in each case, there are infinitely many possible answers since it is possible to find a polynomial of degree 5 (or higher) that will go through each of the above numbers and ANY other number, missing from ANY position.

Using polynomials of order 4, though, there is only one answer for each position. For example,

First number missing: 171

Un= (-27n4+ 422n3- 2364n2+ 5611n - 4668)/6

Last number missing: 218

Un= (-27n4+ 314n3- 1260n2+ 2041n - 1026)/6

Answer 3

9

Answer 4

37