SOLUTION: Hi, could someone please help me with this problem? For a given geometric sequence, all of whose terms are positive real numbers, a_1=2/3 and a_5=1/24. Find a_6.

Algebra ->  Sequences-and-series -> SOLUTION: Hi, could someone please help me with this problem? For a given geometric sequence, all of whose terms are positive real numbers, a_1=2/3 and a_5=1/24. Find a_6.       Log On


   

Question 986777: Hi, could someone please help me with this problem?
For a given geometric sequence, all of whose terms are positive real numbers,
a_1=2/3 and a_5=1/24. Find a_6.
Answer by ikleyn(52909) About Me  (Show Source):
You can put this solution on YOUR website!
.
For a given geometric sequence,  whose terms all are positive real numbers,
a%5B1%5D = 2%2F3  and  a%5B5%5D = 1%2F24.  Find a%5B6%5D.
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a%5B5%5D%2Fa%5B1%5D = q%5E4 = 1%2F24:2%2F3 = 3%2F%2824%2A2%29 = 1%2F16.

Hence,  q = root%284%2C1%2F16%29 = 1%2F2       (Notice that negative q does't fit, because all terms should be positive).

It implies that  a%5B6%5D = a%5B5%5D.1%2F2 = 1%2F24.1%2F2 = 1%2F48.

Answer.  a%5B6%5D = 1%2F48.