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What is the millionth term in the sequence?

+2 votes
How do you find the millionth term in 8,11,16,23,32...?
asked Jul 10, 2014 in Math by luongamanda Evoker (610 points)  

1 Answer

+1 vote

The differences between each pair of consecutive terms seems to go like this:

3, 5, 7, 9, ...

Consider the sequence of perfect squares

1, 4, 9, 16, 25, ...

If we take the differences between each pair of consecutive terms with this sequence, we get:

3, 5, 7, 9, ...

There appears to be a pattern here, where the sequence involves perfect squares.

In order to match up the terms, we can add 7 to each term to get:

7+1 = 8,
7+4 = 11,
7+9 = 16,
7+16 =23,
7+25 =32,
...,
\(7+n^2\)

where n represents the nth term of the sequence. 

Then the millionth term would be...drum roll...

=\(7+(1,000,000)^2\)
= \(7+(10^6)^2\)
= \(7+10^{12}\)
= 1,000,000,000,007 wink

 

answered Jul 15, 2014 by l-johnson Evoker (540 points)  
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