SOLUTION: The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200. A) Find the sum of the first 8 terms b) Find the least value for n which Sn

Algebra ->  Real-numbers -> SOLUTION: The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200. A) Find the sum of the first 8 terms b) Find the least value for n which Sn       Log On


   

Question 1185339: The first term of an infinite geometric sequence is 4. The sum of the infinite
sequence is 200.
A) Find the sum of the first 8 terms
b) Find the least value for n which Sn > 163.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A) Find the sum of the first 8 terms
S%5Binfinity%5D%22%22=%22%22a%5B1%5D%2F%281-r%5E%22%22%29

200%22%22=%22%224%5E%22%22%2F%281-r%5E%22%22%29

200%281-r%29%22%22=%22%224

Divide both sides by 4

50%281-r%29%22%22=%22%221

50-50r%22%22=%22%221

-50r%22%22=%22%22-49

r%22%22=%22%2249%2F50

r%22%22=%22%220.98

S%5Bn%5D%22%22=%22%22a%5B1%5D%281-r%5En%29%2F%281-r%5E%22%22%29

S%5B8%5D%22%22=%22%224%281-0.98%5E8%29%2F%281-0.98%5E%22%22%29

S%5B8%5D%22%22=%22%2229.84739548

b) Find the least value for n which Sn > 163.

S%5Bn%5D%22%22=%22%224%281-0.98%5En%29%2F%281-0.98%5E%22%22%29%22%22%3E%22%22163

%284%2F.02%29%281-0.98%5En%29%22%22%3E%22%22163

200%281-0.98%5En%29%22%22%3E%22%22163

1-0.98%5En%22%22%3E%22%22163%2F200

1-0.98%5En%22%22%3E%22%220.815

-0.98%5En%22%22%3E%22%22-0.185

0.98%5En%22%22%3E%22%220.185

Take natural logs of both side:

ln%280.98%5En%29%22%22%3E%22%22ln%280.185%29

n%2Aln%280.98%29%22%22%3E%22%22ln%280.185%29

n%22%22%3E%22%22ln%280.185%29%2Fln%280.98%29

n%22%22%3E%22%2283.52343215

The least integer than n can take on greater 
than that is 84.

Edwin