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.
When n = 1, sequence term (call it y) = 7. Each unit increase in n results in an increase of 6 in y, so when n = 5, y = 31. Sequence is therefore 7, 13, 19, 25, 31 etc.
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.
There are very many possible solutions. The simplest polynomial solution is t(n) = (n^4 - 14n^3 + 71n^2 + 14n + 24)/24.
There are infinitely many possible answers. the simplest polynomial is Un = -n4 + 12n3 - 47n2 + 78n - 41
5 to 7 is 27 to 17 is 1017 to 19 is 219 to 29 is 1029 to 31 is 2there fore following the pattern the nth term is 4131 to 41 is 10
The nth term is 6n+1 and so the next term will be 31
The nth term in the arithmetic progression 10, 17, 25, 31, 38... will be equal to 7n + 3.
10n + 1
2n^2-1
The nth term is 7n-4 and so the next number in the sequence is 31
31 - n
As given, the sequence is too short to establish the generating rule. If the second term was 19 and NOT 29, then the nth term is tn = 6*n + 7 or 6(n+1)+1
The next number is 46. The sequence adds an increasing multiple of 3. 1+3 = 4, 4+6=10, 10+9=19, 19+12=31, and 31+15 = 46. With 1 as the value for n=1, the value for the nth term is x = 1.5 n² - 1.5n + 1 e.g. the 6th term is 1.5 (6x6) - 1.5 (6) + 1 = 54 - 9 + 1 = 46
You can see that all the numbers go up by 7. This means that the first part of the nth term rule for this sequence is 7n. Now, you have to find out how to get from 7 to 3, 14 to 10, 21 to 17 ... this is because we are going up in the 7 times table. To get from the seventh times table to the sequence, you take away four. So the answer is : 7n-4
+9
The pattern is: +11, +15, +19, +23, +27 (4n+7) So, the next number would be: (4*6 + 7) = 24 + 7 = +31 Therefore, the answer is: 105 + 31 = 136