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lavalava
Group Title
The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.
 one year ago
 one year ago
lavalava Group Title
The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.
 one year ago
 one year ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[a, a+d,a+2d,a+3d,a+4d,...\] you got \(a+3d=141\) and \(a+6d=132\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that means \(132141=(a+6d)(a+3d)=3d=9\) and so \(d=3\)
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
okay so then d=4?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
actually \(d=3\)
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
umm please explain!!
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
k lets go slow
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
please and thanks
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
actually before we even start, since \(132<141\) is it clear that the terms are getting smaller?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
in other words, "\(d\)" the "common difference" must be negative right?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if we call the first term \(a\) then the second term is \(a+d\) for some \(d\) and the third term is \(a+2d\), the fourth term is \(a+3d\) the fifth term is \(a+4d\) etc
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
in other words, you keep adding \(d\) to each term to get the next term, with the sophistication that you might be "adding" a negative number
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
The fourth term of an arithmetic sequence is 141 tells you that \(a+3d=141\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you see that it is the fourth term, so it is \(a+3d\) not \(a+4d\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
and the seventh term is 132 means \[a+6d=132\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
from these two pieced of information we can solve for \(d\) and then solve for \(a\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
*pieces
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
a bit of algebra shows that \[a+6d(a+3d)=3d\] right?
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
ohh okay i get it..
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so we see that \[3d=132141=9\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
so far so good?
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
and so since it is 74= 3 then 9/3 would be 3 right? giving us the difference
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yeah \(3\) is the difference
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
what you said
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
ohhh okay!!! i get it!! :D
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you are still not done though right?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
your question asked "The first term is _____"
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
hmm well pluggin in the difference and then your equation... a4=141 a3=141+3=144 a2=144+3=147 a1=147+3=150 so then the first term would be 150 right? i just did it backwards
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yeah i guess so i would have said \(a+3\times (3)=141\)or \[a9=141\] making \(a=150\) your method means you understand what is going on, which is good but you certainly wouldn't want to use that if you had say \(a_{75}\) and wanted \(a_1\)
 one year ago

lavalava Group TitleBest ResponseYou've already chosen the best response.1
:D yay thank you!!! :D ohh okay... ill keep in mind that equation!! thank you soo much!
 one year ago
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