SOLUTION: In a geometric sequence, the first term is 3 and the sixth term is 96. a. Find the common ratio b. Find the least value of n such that Un > 3000

Algebra ->  Sequences-and-series -> SOLUTION: In a geometric sequence, the first term is 3 and the sixth term is 96. a. Find the common ratio b. Find the least value of n such that Un > 3000      Log On


   

Question 991377: In a geometric sequence, the first term is 3 and the sixth term is 96.
a. Find the common ratio
b. Find the least value of n such that Un > 3000
Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
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1. a%5B1%5D = 3,

a%5B6%5D = a%5B1%5D%2Aq%5E5,

q%5E5 = a%5B6%5D%2Fa%5B1%5D = 96%2F3 = 32 = 2%5E5,

q = root%285%2C32%29 = 2.

2. a%5B11%5D = 3%2A2%5E10 = 3%2A1024 > 3000.

a%5B10%5D = 3%2A2%5E9 = 3%2A512 < 3000.

n = 11.