please help me on how to solve this question

For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find

a)the possible values of the common ratio

b)the 6th term of the geometric progression.

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- Dec 23rd 2009, 04:31 AMmastermin346Progressions
please help me on how to solve this question

For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find

a)the possible values of the common ratio

b)the 6th term of the geometric progression. - Dec 23rd 2009, 04:42 AMI-Think
G.P.:$\displaystyle \Sigma{ar^k}$

First term:6 $\displaystyle \rightarrow{ar^0=6}$

Hence $\displaystyle a=6$

I assume you mean 1st 3 terms

$\displaystyle a+ar+ar^2=126$

$\displaystyle 6r^2+6r+6=126$

$\displaystyle r^2+r+1=21$

Solve this quadratic equation for your answer

Part b

6th term:$\displaystyle ar^5$

With value of a and r, insert for answer - Dec 23rd 2009, 04:44 AMskeeter
- Dec 23rd 2009, 04:46 AMgalactusQuote:

For a geometric progression,the first term is 6 and the sum of the 3 terms is 126.Find

Quote:

a)the possible values of the common ratio

So, the sum of the first 3 terms is given as $\displaystyle S_{3}=126$ and the first term is $\displaystyle a_{1}=6$

Solve $\displaystyle 126=6\cdot \frac{1-r^{3}}{1-r}\Rightarrow 126=6(r^{2}+r+1)$ for r.

Quote:

b)the 6th term of the geometric progression.