SOLUTION: The sum of the second and third terms of a geometric sequence is 18 . If the tenth term is 8 times the seventh term , find ; a) the first term b) the common ratio c) the sixt

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Question 1176215: The sum of the second and third terms of a geometric sequence is 18 . If the tenth term is 8 times the seventh term , find ;
a) the first term
b) the common ratio
c) the sixth term
Found 3 solutions by CubeyThePenguin, ikleyn, josgarithmetic:
Answer by CubeyThePenguin(3113)   (Show Source):
You can put this solution on YOUR website!
First term = a, common ratio = r

ar + ar^2 = 18
ar^9 = 8(ar^6)

We get r^3 = 2, so r = 2 and a = 3.

sixth term = ar^5 = 3(2)^5 = 96.

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
The sum of the second and third terms of a geometric sequence is 18 . If the tenth term is 4 times the seventh term , find ;
a) the first term
b) the common ratio
c) the sixth term
~~~~~~~~~~~~

The solution by @CubeyThePenguin is TOTALLY WRONG.

For your safety, ignore his post   //   until he fix it (!)

//////////////

Also notice that @josgarithmetic CHANGED the original numbers in your post,
replacing the original piece   " If the tenth term is 4 times the seventh term "
by   "If the tenth term is 8 times the seventh term"

                    W I T H O U T   any   A C N O L E D G M E N T.

                            So be A W A R E   (!)

Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website!
a, the first term
ar, the second term
ar^2, the third term
and then the TENTH term is ar^9.

Taking the second equation,

First Term:

and maybe you can find the sixth term.
.
.