How do you find the nth to the quadratic sequence of 3,8,15,24,35
1 answer:
Having the first term of the sequence
<span>a<span>(0)</span>=3</span>
<span>a<span>(1)</span>=3+5=8</span>
We realized that
<span>a<span>(1)</span>=a<span>(0)</span>+2⋅2+1</span>
We also have :
<span>a<span>(2)</span>=a<span>(1)</span>+2⋅3+1=8+7=15</span>
<span>a<span>(3)</span>=a<span>(2)</span>+2⋅4+1=15+9=24</span>
From above we can realize that each term is the sum of the previous
term and 2*(sequence coefficient added to 1) and 1
So the nth term will be:
<span>a<span>(n)</span>=a<span>(n−1)</span>+2⋅<span>(n+1)</span>+<span>1
</span></span>
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