Question 912611
f(1) = 1 and f(n) = 2*f(n-1)


The idea is to find f(12). We can't do this directly since we're given this recursive sequence. We need to know f(1), f(2), ..., f(10), f(11) before we can determine f(12).


So plug in n = 2, n = 3, etc into f(n) = 2*f(n-1) to find f(2), ..., f(10), f(11)


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f(n) = 2*f(n-1)


f(2) = 2*f(2-1)


f(2) = 2*f(1)


f(2) = 2*1


f(2) = 2



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f(n) = 2*f(n-1)


f(3) = 2*f(3-1)


f(3) = 2*f(2)


f(3) = 2*2


f(3) = 4



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f(n) = 2*f(n-1)


f(4) = 2*f(4-1)


f(4) = 2*f(3)


f(4) = 2*4


f(4) = 8



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f(n) = 2*f(n-1)


f(5) = 2*f(5-1)


f(5) = 2*f(4)


f(5) = 2*8


f(5) = 16



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f(n) = 2*f(n-1)


f(6) = 2*f(6-1)


f(6) = 2*f(5)


f(6) = 2*16


f(6) = 32



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f(n) = 2*f(n-1)


f(7) = 2*f(7-1)


f(7) = 2*f(6)


f(7) = 2*32


f(7) = 64



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f(n) = 2*f(n-1)


f(8) = 2*f(8-1)


f(8) = 2*f(7)


f(8) = 2*64


f(8) = 128



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f(n) = 2*f(n-1)


f(9) = 2*f(9-1)


f(9) = 2*f(8)


f(9) = 2*128


f(9) = 256



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f(n) = 2*f(n-1)


f(10) = 2*f(10-1)


f(10) = 2*f(9)


f(10) = 2*256


f(10) = 512



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f(n) = 2*f(n-1)


f(11) = 2*f(11-1)


f(11) = 2*f(10)


f(11) = 2*512


f(11) = 1024



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f(n) = 2*f(n-1)


f(12) = 2*f(12-1)


f(12) = 2*f(11)


f(12) = 2*1024


f(12) = 2048



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The first twelve terms are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048


The 12th term is <font color="red">2048</font> which is the final answer


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>
or you can visit my website here: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a>


Thanks,


Jim