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anonymous
 3 years ago
The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.
anonymous
 3 years ago
The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[a, a+d,a+2d,a+3d,a+4d,...\] you got \(a+3d=141\) and \(a+6d=132\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that means \(132141=(a+6d)(a+3d)=3d=9\) and so \(d=3\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0actually before we even start, since \(132<141\) is it clear that the terms are getting smaller?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in other words, "\(d\)" the "common difference" must be negative right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The fourth term of an arithmetic sequence is 141 tells you that \(a+3d=141\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you see that it is the fourth term, so it is \(a+3d\) not \(a+4d\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and the seventh term is 132 means \[a+6d=132\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0from these two pieced of information we can solve for \(d\) and then solve for \(a\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0a bit of algebra shows that \[a+6d(a+3d)=3d\] right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so we see that \[3d=132141=9\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and so since it is 74= 3 then 9/3 would be 3 right? giving us the difference

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah \(3\) is the difference

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ohhh okay!!! i get it!! :D

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you are still not done though right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0your question asked "The first term is _____"

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0hmm 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah 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 \(a_1\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0:D yay thank you!!! :D ohh okay... ill keep in mind that equation!! thank you soo much!
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