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

Algebra.Com
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(52777)   (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(39617)   (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.
.
.

RELATED QUESTIONS

The second term of the geometric sequence is 250, and the fifth term is 16. Find the... (answered by ikleyn)
The second term of the geometric sequence is 250, and the fifth term is 16. Find the... (answered by ikleyn)
Find the tenth term of a geometric sequence if the third term is 24 and the fifth term is (answered by josgarithmetic,ikleyn)
The seventh term of a geometric sequence is twice the fifth term and the sum of the first (answered by ikleyn)
if seventh term of geometric sequence is 64 and sum of first ten terms is 1023 then find... (answered by richwmiller)
The first,third and fifth terms of a geometric sequence form arithmetic sequence.If the... (answered by Edwin McCravy)
The first term of a geometric sequence is 9 and the third term is 4. Find the possible... (answered by fcabanski)
The seventh term of an arithmetic sequence is 25. Its first, third, and 21st term form... (answered by greenestamps)
A. In a arithmetic progression, the seventh term is six times the third term and the sum... (answered by MathTherapy)