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

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

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

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

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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1if 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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1in 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

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

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

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

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

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

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

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

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

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

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

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

lavalava
 one year ago
Best ResponseYou've already chosen the best response.1hmm 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

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1yeah 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 \(a_1\)

lavalava
 one year ago
Best 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!
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