Question

How do you find the nth term formula 3,8,15,24,... ?

Answer 1

`a(n) = a(n-1) +2*(n+1)+1`

Explanation:

Having the first term of the sequence
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`a(0) =3`
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`a(1) = 3+5 =8`
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We realized that
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`a(1)= a(0) + 2*2+1`

We also have :
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`a(2) = a(1) + 2*3 +1 = 8 + 7 =15`
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`a(3) = a(2) + 2*4 +1= 15 +9 =24`

From above we can realize that each term is the sum of the previous
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term and 2*(sequence coefficient added to 1) and 1
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So the nth term will be:
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`a(n) =a(n-1) +2*(n+1)+1`