# Fibonacci sequence

• Sep 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.
• Sep 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 \$\displaystyle a_1 = 28,\$ you substitute it into the formula \$\displaystyle a_{k+1}=a_k-4\$ to find \$\displaystyle a_2\$

\$\displaystyle
a_2=28-4 = 24
\$

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

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

\$\displaystyle
a_2=28-4 = 24
\$

Now your \$\displaystyle a_k=24\$, so substitute it in: \$\displaystyle 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??
• Sep 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??

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

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

its clear like water now thank you.