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n2 + 3n - 2
Wiki User
∙ 13y ago
Jason Huang
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.
Ahmed Saleem
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.
Anonymous
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58
