help me with sequences problem.So if the sequence is 2,5,10,17,26

+3 +5 +7 +9 1st difference
+2 +2 +2 2nd difference
then the nth term can be worked out by writing out :
n 1 2 3 4
n squared 1 4 9 16
original sequence 2 5 10 17
nth term= n squared+1

but what about this question:
8, 10, 14, 20, 28
+2 +4 +6 +8
+2 +2 +2

n 1 2 3 4
n squared 1 4 9 16
original sequence 8 10 14 20 the number you have to add to n squared is different every time so does anybody know how too get the nth term for this sequence?

help me with sequences problem.So if the sequence is 2,5,10,17,26

+3 +5 +7 +9 1st difference
+2 +2 +2 2nd difference
then the nth term can be worked out by writing out :
n 1 2 3 4
n squared 1 4 9 16
original sequence 2 5 10 17
nth term= n squared+1

but what about this question:
8, 10, 14, 20, 28
+2 +4 +6 +8
+2 +2 +2

n 1 2 3 4
n squared 1 4 9 16
original sequence 8 10 14 20 the number you have to add to n squared is different every time so does anybody know how too get the nth term for this sequence?

With 2nd differences being equal, the general expression is of the form an^2 + bn + c

8, 10, 14, 20, 28
.+2. +4. +6. +8
...+2. +2. +2

a(1)^2 + b(1) + c = 8
a(2)^2 + b(2) + c = 10
a(3)^2 + b(3) + c = 14

a + b + c = 8
4a + 2b + c = 10
9a + 3b + c = 14

Solving, a = 1, b = -1 and c = 8.

Thus, the nth term derives from N = n^2 - n + 8.

To find the nth term of the sequence 8, 10, 14, 20, 28, we can follow a similar approach as shown in the previous sequence.

First, let's calculate the differences between consecutive terms:

+2 +4 +6 +8

Now, let's calculate the differences between these differences:

+2 +2 +2

Based on the differences, we can see that there is a constant increase of +2 between each term of the differences. This suggests that the nth term of the original sequence is likely to involve adding a multiple of 2 to some function of n.

Now, let's examine the differences between the original sequence and the squares of n:

n 1 2 3 4
n squared 1 4 9 16
original sequence 8 10 14 20

You can observe that by subtracting the squares of n from the original sequence, we get a pattern: 8 - 1 = 7, 10 - 4 = 6, 14 - 9 = 5, 20 - 16 = 4.

Now, let's try adding these results to the squares of n:

n 1 2 3 4
n squared 1 4 9 16
difference 7 6 5 4
original sequence 8 10 14 20

You can see that by adding the differences to the squares of n, we obtain the original sequence.

Therefore, the nth term of the sequence can be obtained by adding the difference (n - n squared) to the square of n:

nth term = n squared + (n - n squared)

Now, you can substitute any value of n to find the corresponding term in the sequence.