Fibonacci sequence

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September 26th 2009, 07:46 PM
flexus

Fibonacci sequence

Write the first five terms of the sequence defined recursively.

a1= 28, ak+1= ak -4

ok i honestly don't understand this at all. i tried to mimic the way the book did it in the example but it did not match the answers in the back of the book. can someone please explain to me how to solve this problem at least give me show me how to do the first two terms. any help is appreciated.
September 26th 2009, 08:08 PM
Roam

Quote:

Originally Posted by flexus

Write the first five terms of the sequence defined recursively.

a1= 28, ak+1= ak -4

ok i honestly don't understand this at all. i tried to mimic the way the book did it in the example but it did not match the answers in the back of the book. can someone please explain to me how to solve this problem at least give me show me how to do the first two terms. any help is appreciated.

Since $a_1 = 28,$ you substitute it into the formula $a_{k+1}=a_k-4$ to find $a_2$

$<br /> a_2=28-4 = 24 <br />$

Now your $a_k=24$ , so substitute it in: $a_3=24-4 = 20$ . Hope that helps.
September 26th 2009, 08:17 PM
flexus

Quote:

Originally Posted by Roam

Since $a_1 = 28,$ you substitute it into the formula $a_{k+1}=a_k-4$ to find $a_2$

$<br /> a_2=28-4 = 24 <br />$

Now your $a_k=24$ , so substitute it in: $a_3=24-4 = 20$ . Hope that helps.

i dont understand how you can substitute 28 into the whole equation of ak+1 ?? how is that possible??
September 26th 2009, 08:26 PM
Roam

Quote:

Originally Posted by flexus

i dont understand how you can substitute 28 into the whole equation of ak+1 ?? how is that possible??

$a_k$ represents "the current value" and $a_{k+1}$ represents the value that comes after your current value. So in this problem you start with $a_1 = 28$ , your initial value is 28. Now you want to find the thing that comes after it (namely $a_2$ ). So you use the given formula $a_{k+1}=a_k-4$ , substitute the current value ( $a_1 =28$ as $a_k$ ) to find the succeeding value ( $a_{k+1} = a_{2}$ ) and so on...
September 26th 2009, 08:28 PM
flexus

Quote:

Originally Posted by Roam

$a_k$ represents "the current value" and $a_{k+1}$ represents the value that comes after your current value. So in this problem you start with $a_1 = 28$ , your initial value is 28. Now you want to find the thing that comes after it (namely $a_2$ ). So you use the given formula $a_{k+1}=a_k-4$ , substitute the current value ( $a_1 =28$ as $a_k$ ) to find the succeeding value ( $a_{k+1} = a_{2}$ ) and so on...

its clear like water now thank you.