A number sequence is shown below.
2,5,10,17,26,37,......
Find a formula for the nth term of the sequence, showing your working clearly.
2,5,10,17,26,37,......
Find a formula for the nth term of the sequence, showing your working clearly.
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n^2 + 1
Find successive differences of the data.
data 2,5,10,17,26,37,......
1rst diff 3 , 5, 7, 9, 11, ...
2nd diff 2, 2, 2 2 2, ...
Since the 2nd differences are constant, the data is a 2nd degree poly, a*n^2+b*n+c
The 1rst diff row has the form a(n+1)^2 + b(n+1) + c - [ a*n^2 + b*n + c] = 2an + b +1
The 2nd diff row has the form 2a(n+1) + b + 1 - [2an + b + 1] = 2*a
From the 1rst entry in the 2nd diff row we get 2*a = 2 and so a = 1
From the 1rst entry in the 1rst diff row we get 2an + b +1 = 3 so b = 0 by using a=1 and n=1
From the 1rst entry in the data row we get a*n^2+b*n+c = 2 so c=1 by using a=1, b=0 and n=1
Find successive differences of the data.
data 2,5,10,17,26,37,......
1rst diff 3 , 5, 7, 9, 11, ...
2nd diff 2, 2, 2 2 2, ...
Since the 2nd differences are constant, the data is a 2nd degree poly, a*n^2+b*n+c
The 1rst diff row has the form a(n+1)^2 + b(n+1) + c - [ a*n^2 + b*n + c] = 2an + b +1
The 2nd diff row has the form 2a(n+1) + b + 1 - [2an + b + 1] = 2*a
From the 1rst entry in the 2nd diff row we get 2*a = 2 and so a = 1
From the 1rst entry in the 1rst diff row we get 2an + b +1 = 3 so b = 0 by using a=1 and n=1
From the 1rst entry in the data row we get a*n^2+b*n+c = 2 so c=1 by using a=1, b=0 and n=1
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list sequential pairs in sequence and subtract each pair how does the difference change
5-2 = 3
10-5 = 5
5-2 = 3
10-5 = 5
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n^2+1