SOLUTION: Enter the 12th term of the sequence for each whole number greater than 1.
f(1) = 1 and f(n) = 2 · f(n − 1)
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Question 912611: Enter the 12th term of the sequence for each whole number greater than 1.
f(1) = 1 and f(n) = 2 · f(n − 1)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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 2048 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 jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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