What is the nth term of 2 8 16 26 38 52?

Answer 1

n2 + 3n - 2

Answer 2

nth term = n*(n+2)+(n-2) when

1st term = 2; 2nd term = 8; 3rd term = 16; 4th term = 26; 5th term = 38; 6th term = 52

Step 1: look at n=3 and 4 and try to come up with a formula that is close

Step 2: first try multiplication for n=3 which should be 16 which is close to 3x5; for n=4 it should be 26 which is close to 4x6

Step 3: so the first part that works is n(n+2) but this only gets us close, not exact

Step4: for n=3 which is 16 is n(n+2)+1; for n=4 it is 26 which is n(n+2)+2

Step 5: so now we can try n(n+2)+(n-2). We test this for n=5 which is 38. 5(5+2)+(5-25) = 38. Test again for n=6 which is 52. 6(6+2)+(6-2) = 52...so all good.

Answer 3

To find the pattern in the sequence 2, 8, 16, 26, 38, 52, we can see that the differences between consecutive terms are increasing by 6, 8, 10, 12, and 14. This indicates that the sequence is following a quadratic pattern. By calculating the second differences, we find that they are constant at 2. Therefore, the nth term of this sequence can be expressed as n^2 + 1.

Answer 4

Well, darling, the nth term of this sequence is n^2 + 1. So, if you plug in n as the position in the sequence, you'll get the corresponding term. Just make sure to start counting from 1, not 0. Happy math-ing!

Answer 5

The given sequence appears to follow a pattern. Let's analyze the differences between consecutive terms:

8 - 2 = 6

16 - 8 = 8

26 - 16 = 10

38 - 26 = 12

52 - 38 = 14

The differences between consecutive terms are increasing by 2 each time. So, to find the next term in the sequence, add 16 (the previous difference) and 2:

14 + 2 = 1614+2=16

Now, add this difference to the last term in the sequence:

52 + 16 = 6852+16=68

Therefore, the next term in the sequence is 68.

Answer 6

87