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lavalava
 2 years ago
The fourth term of an arithmetic sequence is 141, and the seventh term is 132. The first term is _____.
lavalava
 2 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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satellite73
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1that means \(132141=(a+6d)(a+3d)=3d=9\) and so \(d=3\)

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

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

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

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

lavalava
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1yeah \(3\) is the difference

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

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

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

lavalava
 2 years 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
 2 years 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
 2 years 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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