SOLUTION: Help!! Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it. A) Is the sequence formed by the value at the beginning of e

Algebra ->  Sequences-and-series -> SOLUTION: Help!! Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it. A) Is the sequence formed by the value at the beginning of e      Log On


   



Question 850797: Help!! Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it. A) Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain. B) write an explicit formula to represent the sequence. C) find the value of the computer at the beginning of the 6th year.
Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can work it out
Say, for now, that she bought it for +x+ dollars
Let +V+ = the value of the computer after +n+ years
After 1 year:
+V+=+x+-+.1x+
After 2 years:
+V+=+%28+x+-+.1x+%29+-+.1%2A%28+x+-+.1x+%29+
I can factor out +x+-+.1x+
+V+=+%28+x+-+.1x+%29%2A%28+1+-+.1+%29+
Factor out +x+
+V+=+x%2A%28+1+-+.1+%29%5E2+
After 3 years:
+V+=++%28+x%2A%28+1+-+.1+%29%5E2+%29+-+.1%2A%28+x%2A%28+1+-+.1+%29%5E2+%29+
Factor out +x%2A%28+1+-+.1+%29%5E2+
+V+=+%28+x%2A%28+1+-+.1+%29%5E2+%29%2A%28+1+-+.1+%29+
+V+=+x%2A%28+1+-+.1+%29%5E3+
------------------------
This continues every year, so after +n+ years,
+V+=+x%2A%28+1+-+.1+%29%5En+
This is a geometric sequence
+x+=+1250+
+n+=+5+
+V+=+1250%2A%28+.9+%29%5E5+
+V+=+1250%2A.59049+
+V+=+738.11+
After 5 yrs, the computer is worth $738.11

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
(1250,1125, 1012.50,911.25,820.125,738.1125, 664.30125 ..}
Geometric: r = .9
B. a%5Bn%5D+=+a%5B1%5D%28r%29%5E%28n-1%29+
C. a%5B6%5D+=+1250%28.9%29%5E%28n-1%29%29
a%5B6%5D+=+1250%28.9%29%5E5%29 = $738.11