anonymous
  • anonymous
What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = –59?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
hi guyz
apoorvk
  • apoorvk
okay so we know nth term of an AP is a1 + (n-1)d .. here d is the common difference between each term. so, a1=13.... (i) a1 + (13-1)d=-59 ...(ii) Put value of a1 from (i) in (ii) to solve it and get 'd' then find 32nd term by the formula for any nth term!! post what you get and verify, or if you face any problems!
anonymous
  • anonymous
@kmila03 Can you follow apoorvk's instruction?

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anonymous
  • anonymous
mmhm not really im trying ...
anonymous
  • anonymous
a_13 = a_1 + 12d Do you know this formula by now?
anonymous
  • anonymous
actually thats the problem i never seen this before
anonymous
  • anonymous
Memorize this formula, right now just plug number in!
anonymous
  • anonymous
ok, but what is 12d?
anonymous
  • anonymous
d is what we're looking for d = ...
apoorvk
  • apoorvk
d is the variable.. the common difference any two successive terms of an AP that you gotta find!
anonymous
  • anonymous
12d = a_13 - a_1 =>d = (a_13 - a_1) / 12 Can you plug in the numbers now?
anonymous
  • anonymous
so, can you guys do it. so ill see the steps?
apoorvk
  • apoorvk
okay i am continuing from my first post above..... just tell me do you understand linear equations?? did you understand the equations i wrote? and do you understand the question?
anonymous
  • anonymous
yes... so if i plug in the number from =>d = (a_13 - a_1) / 12 is = d=-6 ?
apoorvk
  • apoorvk
that's it kmila!!!!! you got it!!! what was there to be afraid of?? :) now can you find the 32nd term??
anonymous
  • anonymous
thanks :)..... but how can i find 32nd?
apoorvk
  • apoorvk
okay any nth term "Tn" of an AP is Tn=a + (n-1)d where 'a' is the first term and 'd' is the common diff. so, n is 32 here, first term is given and you just found out d. plug in the values and get the answer!
apoorvk
  • apoorvk
it may so happen in future questions that the first term may not be given straightaway, but any two terms say 4th and 6th are provided, in that case you need to form 2 linear equations in 'a' and 'd' and solve to find 'a' and 'd'. then proceed with what the question asks!
anonymous
  • anonymous
so it will be -173?
anonymous
  • anonymous
Yeehhh, you got it :D
apoorvk
  • apoorvk
Riiighttttt-O!!!!!!! there you are!!
anonymous
  • anonymous
ok, thank u guys so much!!!
anonymous
  • anonymous
We hope you learn the formula AND keep PRACTICE :)

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