anonymous
  • anonymous
Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@IrishBoy123
IrishBoy123
  • IrishBoy123
this one is arithmetic, right? so what is the common difference?
anonymous
  • anonymous
5

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IrishBoy123
  • IrishBoy123
yes so \(a_1 = -8\) \(a_2 = -8 + 1(5)\) \(a_3 = -8 + 2(5)\) we will want a general term for \(a_n\), the nth term in this sequence
IrishBoy123
  • IrishBoy123
can you have a go at that?
IrishBoy123
  • IrishBoy123
|dw:1438707453164:dw|
anonymous
  • anonymous
Would it be:\[\sum_{n=0}^{\infty}(-8+5n) \]
anonymous
  • anonymous
@IrishBoy123
IrishBoy123
  • IrishBoy123
if we are starting at n = 1, you need a small tweak
IrishBoy123
  • IrishBoy123
if term 1 is \(a_1\), with \(n = 1\)
anonymous
  • anonymous
sum_{n=0}^{15}(-8+5n) ?
anonymous
  • anonymous
\[\sum_{n=0}^{15}(-8+5n)\]
IrishBoy123
  • IrishBoy123
\(a_1=−8 = -8 +5(1-1)\) \(a_2=−8+(5)(2-1)\) \(a_3=−8+(5)(3-1)\)
IrishBoy123
  • IrishBoy123
\(a_n = ??\)
anonymous
  • anonymous
-8+5n
IrishBoy123
  • IrishBoy123
-8+5(n - ??)
anonymous
  • anonymous
That's not an answer choice though. These are my answer choices: A. \[\sum_{n=0}^{15}(-8+5n)\] B. \[\sum_{n=0}^{\infty}(-40n)\] C.\[\sum_{n-0}^{15}(-40n)\] D. \[\sum_{n=0}^{\infty}(-8+5n)\]
IrishBoy123
  • IrishBoy123
OK, they're doing it that way, with the first term as \(a_0\) not \(a_1\) in which case you go with your suggestion, \(-8+5n\) and checking the value of \(n\) for the last term: \(-8+5n = 67 \implies n = 15\)
anonymous
  • anonymous
Ok thanks! So it would be A?
IrishBoy123
  • IrishBoy123
\( \huge \checkmark \)

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