anonymous
  • anonymous
The 80th term of an arithmetic sequence is twice the 30th term. If the first term is 7, what is the 40th term?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what do you know about arithmetic sequence so far?
anonymous
  • anonymous
what do you mean?
anonymous
  • anonymous
if you have treated arithmetic sequence, what are the formulas relating to an arithmetic sequence do you know?

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anonymous
  • anonymous
idk. we've learned about finding rules from a sequence before. does that make sense?
anonymous
  • anonymous
do you know the following formula? \[\Large a_n =a_1+(n-1)d\] fro finding the nth term of an arithmetic sequence?
anonymous
  • anonymous
no
anonymous
  • anonymous
then you would have difficulties understanding my explanation...
anonymous
  • anonymous
could you try to explain it to me?
anonymous
  • anonymous
okay.. i would try to explain... since the 80th term is twice the 30th term, \[\Large a_{80}=2a_{30}\]
anonymous
  • anonymous
so what does the d in the equation represent?
anonymous
  • anonymous
i would break that down a bit using the formula i gave above... \[\Large a_1+(80-1)d=2(a_1+(30-1)d)\] you were told in the question that the first term of the sequence which is a(1) is 7... so \[\Large 7+79d=2(7+29d)\] \[\Large 7+29d=14+58d\] from there, what do you get when you solve for d??
anonymous
  • anonymous
d represents the common difference between consecutive terms in the sequence.
anonymous
  • anonymous
why did you subtract 1 from 30 and 80?
anonymous
  • anonymous
that is what is in the formula..
anonymous
  • anonymous
i posted the formula above..
anonymous
  • anonymous
i got d=1/3
anonymous
  • anonymous
i made a mistake! it is supposed to be \[\Large 7+79d=14+58d\]
anonymous
  • anonymous
that's what i got and i solved for d.
anonymous
  • anonymous
can you please post your working?
anonymous
  • anonymous
7+(80-1)d=2(7+(30-1)d) 7+79d=2(7+29d) 7+79d=14+58d 21d=7 d=1/3
anonymous
  • anonymous
yh..you are right! i made a mistake!
anonymous
  • anonymous
okay now that you have found d from the information given in the question, you can now find the 40th term using the same formula i posted above.. \[\Large a_{40}=7+(40-1)\times \frac{ 1 }{ 3 }\]
anonymous
  • anonymous
a(40) simply represents the 40th term

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