Nth expression for the following:6,11,17,24,32.....

41 it goes up a number each time

The numbers represent the following sequence

n........1...2...3...4...4...
.........6..11..17..24..32...
1st diff...5...6...7...8
2nd dif......1...1...1

With the 2nd differences equal to 1, the general form of the equation defining the Nth term is a quadratic of the form N = an^2 + bn + c. Using the given data we can write

1 + b + c = 6
4a + 2b + c = 11
9a + 3b + c = 17

Solving yields a = 1/2, b 7/2 and c = 2 making the general expression for the Nth term N = (n^2 + 7n + 4)/2.

Thus, the sequence continues as
6, 11, 17, 24, 32, 41, 51, 62, 74...

To find the expression for the given sequence, we can observe the pattern between the numbers.

Looking closely, we can see that each number in the sequence is obtained by increasing the previous number by a specific amount. Let's find this pattern step by step:

1st term: 6
2nd term: 11 (6 + 5)
3rd term: 17 (11 + 6)
4th term: 24 (17 + 7)
5th term: 32 (24 + 8)

From the differences between the terms, we can see that the pattern is as follows:

1st term: 6
2nd term: 11 (6 + 5)
3rd term: 17 (11 + 6)
4th term: 24 (17 + 7)
5th term: 32 (24 + 8)

By observing the pattern, we can see that the difference between consecutive terms is increasing by 1 with each term.

Now, to find the expression for the nth term, let's derive a general formula using the difference pattern.

Let's call the first term in the sequence "a" and the common difference between consecutive terms "d".

The general formula for this arithmetic sequence is:
nth term = a + (n - 1)d

In this case, the first term is 6 and the common difference is increasing by 1 with each term.

Therefore, the formula for the nth term of the given sequence is:
nth term = 6 + (n - 1)1

Simplifying this equation, we get:
nth term = 6 + n - 1
nth term = n + 5

So, the expression for the given sequence is nth term = n + 5.