The sum of the 3rd term to the 7th term in a geometric series is 3267. Find the first term if the common ratio is 3 [closed]

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The sum of the 3rd term to the 7th term in a geometric series is 3267. Find the first term if the common ratio is 3




Ive been stuck on this question for a while now. I was hoping someone could help?






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closed as off-topic by Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore Sep 9 at 15:50


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    Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
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up vote
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down vote

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The sum of the 3rd term to the 7th term in a geometric series is 3267. Find the first term if the common ratio is 3




Ive been stuck on this question for a while now. I was hoping someone could help?






sequences-and-series algebra-precalculus







share|cite|improve this question















closed as off-topic by Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore Sep 9 at 15:50


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore
If this question can be reworded to fit the rules in the help center, please edit the question.








  • 1




    Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
    – Anik Bhowmick
    Sep 9 at 6:46












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite












The sum of the 3rd term to the 7th term in a geometric series is 3267. Find the first term if the common ratio is 3




Ive been stuck on this question for a while now. I was hoping someone could help?






sequences-and-series algebra-precalculus







share|cite|improve this question
















The sum of the 3rd term to the 7th term in a geometric series is 3267. Find the first term if the common ratio is 3




Ive been stuck on this question for a while now. I was hoping someone could help?






sequences-and-series algebra-precalculus




sequences-and-series algebra-precalculus






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share|cite|improve this question













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edited Sep 9 at 6:27









Eric Wofsey

167k12196310




167k12196310










asked Sep 9 at 6:18









C.lea

1




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closed as off-topic by Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore Sep 9 at 15:50


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore Sep 9 at 15:50


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Eric Wofsey, Nosrati, Jendrik Stelzner, user91500, Learnmore
If this question can be reworded to fit the rules in the help center, please edit the question.







  • 1




    Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
    – Anik Bhowmick
    Sep 9 at 6:46












  • 1




    Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
    – Anik Bhowmick
    Sep 9 at 6:46







1




1




Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
– Anik Bhowmick
Sep 9 at 6:46




Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :)
– Anik Bhowmick
Sep 9 at 6:46










2 Answers
2






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$S(n) = fraca(r^n-1)r-1$ where $r=3$ and $a$ is to be determined.



Sum from third to seventh terms inclusive = $S(7)-S(2)$.



You now have a single variable linear equation to solve. What's the problem?






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    up vote
    0
    down vote













    Lets say the first term is $a$



    given $r=3$



    $$a_3+a_4+cdots+a_7=3267$$
    $$a_1+a_2+a_3+cdots+a_7=fraca(3^7-1)3-1$$
    $$a_3+cdots+a_7=fraca(3^7-1)3-1-a_1-a_2$$
    $$3267=1093cdot a-a-3cdot a$$






    share|cite|improve this answer





























      2 Answers
      2






      active

      oldest

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      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      1
      down vote













      $S(n) = fraca(r^n-1)r-1$ where $r=3$ and $a$ is to be determined.



      Sum from third to seventh terms inclusive = $S(7)-S(2)$.



      You now have a single variable linear equation to solve. What's the problem?






      share|cite|improve this answer
























        up vote
        1
        down vote













        $S(n) = fraca(r^n-1)r-1$ where $r=3$ and $a$ is to be determined.



        Sum from third to seventh terms inclusive = $S(7)-S(2)$.



        You now have a single variable linear equation to solve. What's the problem?






        share|cite|improve this answer






















          up vote
          1
          down vote










          up vote
          1
          down vote









          $S(n) = fraca(r^n-1)r-1$ where $r=3$ and $a$ is to be determined.



          Sum from third to seventh terms inclusive = $S(7)-S(2)$.



          You now have a single variable linear equation to solve. What's the problem?






          share|cite|improve this answer












          $S(n) = fraca(r^n-1)r-1$ where $r=3$ and $a$ is to be determined.



          Sum from third to seventh terms inclusive = $S(7)-S(2)$.



          You now have a single variable linear equation to solve. What's the problem?







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Sep 9 at 6:34









          Deepak

          16.2k11437




          16.2k11437




















              up vote
              0
              down vote













              Lets say the first term is $a$



              given $r=3$



              $$a_3+a_4+cdots+a_7=3267$$
              $$a_1+a_2+a_3+cdots+a_7=fraca(3^7-1)3-1$$
              $$a_3+cdots+a_7=fraca(3^7-1)3-1-a_1-a_2$$
              $$3267=1093cdot a-a-3cdot a$$






              share|cite|improve this answer


























                up vote
                0
                down vote













                Lets say the first term is $a$



                given $r=3$



                $$a_3+a_4+cdots+a_7=3267$$
                $$a_1+a_2+a_3+cdots+a_7=fraca(3^7-1)3-1$$
                $$a_3+cdots+a_7=fraca(3^7-1)3-1-a_1-a_2$$
                $$3267=1093cdot a-a-3cdot a$$






                share|cite|improve this answer
























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Lets say the first term is $a$



                  given $r=3$



                  $$a_3+a_4+cdots+a_7=3267$$
                  $$a_1+a_2+a_3+cdots+a_7=fraca(3^7-1)3-1$$
                  $$a_3+cdots+a_7=fraca(3^7-1)3-1-a_1-a_2$$
                  $$3267=1093cdot a-a-3cdot a$$






                  share|cite|improve this answer














                  Lets say the first term is $a$



                  given $r=3$



                  $$a_3+a_4+cdots+a_7=3267$$
                  $$a_1+a_2+a_3+cdots+a_7=fraca(3^7-1)3-1$$
                  $$a_3+cdots+a_7=fraca(3^7-1)3-1-a_1-a_2$$
                  $$3267=1093cdot a-a-3cdot a$$







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Sep 9 at 9:24

























                  answered Sep 9 at 9:18









                  Deepesh Meena

                  4,20621025




                  4,20621025












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