Arithmetic sequence check my work

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Let $a_j$ be an arithmetic sequence with the following conditions:




Given $s_16 = 376$ and $a_16 = 46$, find $a_1$.



$$s_n = fracn2 cdot(a_1 + a_n) $$




$376 = dfrac162 cdot (a_1 + 46)$
$47 - 46 = 1$
$a_1 = 1$



common ratio $= -5$?



Don't need that value however.






algebra-precalculus arithmetic







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  • $a_1$ is correct, $d=5$. What was the question in this exercise?
    – user376343
    4 hours ago










  • It was to find a1
    – UsuallyStuckOnMath
    4 hours ago














up vote
2
down vote

favorite












Let $a_j$ be an arithmetic sequence with the following conditions:




Given $s_16 = 376$ and $a_16 = 46$, find $a_1$.



$$s_n = fracn2 cdot(a_1 + a_n) $$




$376 = dfrac162 cdot (a_1 + 46)$
$47 - 46 = 1$
$a_1 = 1$



common ratio $= -5$?



Don't need that value however.






algebra-precalculus arithmetic







share|cite|improve this question









New contributor




UsuallyStuckOnMath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.



















  • $a_1$ is correct, $d=5$. What was the question in this exercise?
    – user376343
    4 hours ago










  • It was to find a1
    – UsuallyStuckOnMath
    4 hours ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











Let $a_j$ be an arithmetic sequence with the following conditions:




Given $s_16 = 376$ and $a_16 = 46$, find $a_1$.



$$s_n = fracn2 cdot(a_1 + a_n) $$




$376 = dfrac162 cdot (a_1 + 46)$
$47 - 46 = 1$
$a_1 = 1$



common ratio $= -5$?



Don't need that value however.






algebra-precalculus arithmetic







share|cite|improve this question









New contributor




UsuallyStuckOnMath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Let $a_j$ be an arithmetic sequence with the following conditions:




Given $s_16 = 376$ and $a_16 = 46$, find $a_1$.



$$s_n = fracn2 cdot(a_1 + a_n) $$




$376 = dfrac162 cdot (a_1 + 46)$
$47 - 46 = 1$
$a_1 = 1$



common ratio $= -5$?



Don't need that value however.






algebra-precalculus arithmetic




algebra-precalculus arithmetic






share|cite|improve this question









New contributor




UsuallyStuckOnMath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











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UsuallyStuckOnMath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 4 hours ago









amWhy

191k27223436




191k27223436






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asked 4 hours ago









UsuallyStuckOnMath

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285




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UsuallyStuckOnMath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Check out our Code of Conduct.











  • $a_1$ is correct, $d=5$. What was the question in this exercise?
    – user376343
    4 hours ago










  • It was to find a1
    – UsuallyStuckOnMath
    4 hours ago
















  • $a_1$ is correct, $d=5$. What was the question in this exercise?
    – user376343
    4 hours ago










  • It was to find a1
    – UsuallyStuckOnMath
    4 hours ago















$a_1$ is correct, $d=5$. What was the question in this exercise?
– user376343
4 hours ago




$a_1$ is correct, $d=5$. What was the question in this exercise?
– user376343
4 hours ago












It was to find a1
– UsuallyStuckOnMath
4 hours ago




It was to find a1
– UsuallyStuckOnMath
4 hours ago










2 Answers
2






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up vote
3
down vote



accepted










Your approach is correct, but it would be better to write it something like $$376=frac 162(a_1+46)\frac 3768=a_1+46\1=a_1$$
Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.



The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.






share|cite|improve this answer




















  • Thank you for the help and I agree.
    – UsuallyStuckOnMath
    4 hours ago

















up vote
1
down vote













After $376 = dfrac162 cdot (a_1 + 46)$ you get, $a_1+ 46=376times frac216$ or, $a_1=47-46=1$ so finally you get $a_1=1$.






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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote



    accepted










    Your approach is correct, but it would be better to write it something like $$376=frac 162(a_1+46)\frac 3768=a_1+46\1=a_1$$
    Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.



    The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.






    share|cite|improve this answer




















    • Thank you for the help and I agree.
      – UsuallyStuckOnMath
      4 hours ago














    up vote
    3
    down vote



    accepted










    Your approach is correct, but it would be better to write it something like $$376=frac 162(a_1+46)\frac 3768=a_1+46\1=a_1$$
    Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.



    The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.






    share|cite|improve this answer




















    • Thank you for the help and I agree.
      – UsuallyStuckOnMath
      4 hours ago












    up vote
    3
    down vote



    accepted







    up vote
    3
    down vote



    accepted






    Your approach is correct, but it would be better to write it something like $$376=frac 162(a_1+46)\frac 3768=a_1+46\1=a_1$$
    Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.



    The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.






    share|cite|improve this answer












    Your approach is correct, but it would be better to write it something like $$376=frac 162(a_1+46)\frac 3768=a_1+46\1=a_1$$
    Your statement that $47-46=1$ is correct, but is not motivated. This is why we keep the variables in the equations.



    The difference (not common ratio) is $5$, not $-5$ as the terms are increasing.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 4 hours ago









    Ross Millikan

    284k23192361




    284k23192361











    • Thank you for the help and I agree.
      – UsuallyStuckOnMath
      4 hours ago
















    • Thank you for the help and I agree.
      – UsuallyStuckOnMath
      4 hours ago















    Thank you for the help and I agree.
    – UsuallyStuckOnMath
    4 hours ago




    Thank you for the help and I agree.
    – UsuallyStuckOnMath
    4 hours ago










    up vote
    1
    down vote













    After $376 = dfrac162 cdot (a_1 + 46)$ you get, $a_1+ 46=376times frac216$ or, $a_1=47-46=1$ so finally you get $a_1=1$.






    share|cite|improve this answer


























      up vote
      1
      down vote













      After $376 = dfrac162 cdot (a_1 + 46)$ you get, $a_1+ 46=376times frac216$ or, $a_1=47-46=1$ so finally you get $a_1=1$.






      share|cite|improve this answer
























        up vote
        1
        down vote










        up vote
        1
        down vote









        After $376 = dfrac162 cdot (a_1 + 46)$ you get, $a_1+ 46=376times frac216$ or, $a_1=47-46=1$ so finally you get $a_1=1$.






        share|cite|improve this answer














        After $376 = dfrac162 cdot (a_1 + 46)$ you get, $a_1+ 46=376times frac216$ or, $a_1=47-46=1$ so finally you get $a_1=1$.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited 4 hours ago

























        answered 4 hours ago









        tarit goswami

        1,710220




        1,710220




















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