SOLUTION: Find the value of x so that x+2, 5x+1, x+11 will form a geometric sequence. Find the sum of the first 10 terms of the given sequence.

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Question 1041809: Find the value of x so that x+2, 5x+1, x+11 will form a geometric sequence. Find the sum of the first 10 terms of the given sequence.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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Find x from the condition  a%5B3%5D%2Fa%5B2%5D = a%5B2%5D%2Fa%5B1%5D which is direct definition of a geometric progression.

It gives you 

a%5B2%5D%5E2 = a%5B1%5D%2Aa%5B3%5D,

which is translated/converted into the equation

%285x%2B1%29%5E2 = (x+2)*(x+11).

Simplify and solve it for x (which is just arithmetic).

Find x and all three terms.

Then find the rest.