It appears to increase by 9 each time, which is characterized in 2 digit numbers by the left digit increasing by one while the right digit decreases by one. Using this pattern, it can be deduced that the next number in the sequence is 62.
Any number can be the nth number. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest polynomial, of order 3, is
T(n) = n^2 - 2n + 3 for n = 1, 2, 3, ...
It is: nth term = 35-9n
35 * * * * * That is the next term. The question, however, is about the nth term. And that is 6*n - 1
It is 6n+5 and so the next term will be 35
The common difference (d) between successive terms is -9. The first term (a) is 26 The formula for the nth term [a(n)] of an Arithmetic Series is , a + (n - 1)d. Inputting the values for a and d gives :- a(n) = 26 - 9(n - 1) = 26 - 9n + 9 = 35 - 9n......where n = 1,2,3......
The given sequence (7, 14, 21, 28, 35,....) is an arithmetic sequence where each term increases by 7. The nth term of the given sequence is 7n
n + 6 * * * * * I suggest you try t(n) = 6n + 5 instead.
35
(n+1)2-1
35
The answer is -26. -26 x -2 = 52 52 - 17 = 35
t(n) = n2 + 5n - 1
Say if you had the pattern 15 20 25 30 35 40 45 50 To find the nth term you have to see what the gap between the numbers is. In our case this is 5. Then you have to find out what the difference between the gap and the first number. In this sequence it is 10. So your answer would be..... 5n+10 That's how you find the nth term.