# A bank account...

• May 31st 2008, 05:05 PM
gumi
A bank account...
a bank account pays 3% interest. Suppose you invest \$2000 in such an account.
Let a(n) be the amount in the account after n years. So a1=2000+0.03*2000=2060 and a2=2060+0.03*2060=2121.80. Find a3 and a4?

Is this sequence an arithmetic sequence, geometric sequence or neither? and why?

Find a10
• May 31st 2008, 07:31 PM
james21
well i know it is not arithmetic but i'm not so sure about what exactly, and is this simple or compound interest
• May 31st 2008, 11:35 PM
Moo
Hello,

Quote:

Originally Posted by gumi
a bank account pays 3% interest. Suppose you invest \$2000 in such an account.
Let a(n) be the amount in the account after n years. So a1=2000+0.03*2000=2060 and a2=2060+0.03*2060=2121.80. Find a3 and a4?

Is this sequence an arithmetic sequence, geometric sequence or neither? and why?

Find a10

You should see it this way :

\$\displaystyle a_1=2000+0.03*2000=2000(1+0.03)=2000*1.03\$

\$\displaystyle a_2=(2000*1.03)+(2000*1.03)*0.03=(2000*1.03)(1+0.0 3)=2000*1.03^2\$

It's a geometric sequence (Wink)
• May 31st 2008, 11:37 PM
Dr Zoidburg
since a2 uses a1 in it's equation, it makes it a geometric sequence.
You can see the difference between the two here:
Arithmetic and Geometric series

It's compound interest since you're taking 3% of whatever the last total is and not just 3% of the initial amount
a3 is easy: 2121.80+0.03*2121.80 = 2185.45
You could just write it as 2121.80*1.03, or even \$\displaystyle 2000*1.03^3\$

The series is \$\displaystyle 2000*1.03^n\$ where n = years in account.