anonymous
  • anonymous
Find the next three terms of the sequence –8, 24, –72, 216, . . . A) 648, –1944, 5832 B) 248, –616, 248 C) –648, 1944, –5832 D) 216, –648, 1944
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Okay. This is probably an awful way to teach this, but this is how I learned. –8, 24, –72, 216, . . . What I would do is I would first divide 24 and -8 You would get -3. Then try it. -8 x -3 = 24 24 x -3 = -72 Do you understand?
anonymous
  • anonymous
Yeah so like the number is -3 and -8*-3 = 24 and 24*-3 = -72 and -72*-3= 216 and so on.. @elite.weeaboo
anonymous
  • anonymous
Correct (:

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anonymous
  • anonymous
216*-3= -648, -648*-3= 1944, 1944*-3= -5832
anonymous
  • anonymous
the answer is C
anonymous
  • anonymous
I would think so.
anonymous
  • anonymous
Wait until idku is done typing. I could be wrong.
idku
  • idku
Oh, no it is correct, i was just going to make a definitional [ost.
idku
  • idku
just a brief post about the definitions: A sequence that follows such a pattern (multiplying a term times some number to find the next term), is called a "geometric sequence". This number -3, is the number by which you multiply to find the next term - and it is called "common ratio" (denoted by letter r). So you can say in your case "r=-3" \(a_1\) is a notation for the first term \(a_2\) is a notation for the second term \(a_3\) is a notation for the third term so on..... \(a_n\) is a notation for some \(\rm n\)th term So in a geometric sequence (like yours) you should see that: \(a_1 \times r = a_2\) agree? \(a_2 \times r = a_3\) or \(a_1 \times r \times r ~~= a_1 \times r^2= a_3\) agree? \(a_3 \times r = a_4\) or \(a_1 \times r \times r \times r~~= a_1 \times r^3= a_4\) and thus.... \(a_1 \times r^{n-1} = a_n \)
idku
  • idku
So if you wanted to find 1000th term of your sequence, you would go: \(a_1 \times r^{n-1} = a_n \) \(a_1 \times r^{1000-1} = a_{1000} \) your first term is -8, so: \((-8) \times r^{1000-1} = a_{1000} \) your common ratio is -3: \((-8) \times (-3)^{1000-1} = a_{1000} \) \(\color{blue}{(-8) \times (-3)^{999} = a_{1000}} \)
anonymous
  • anonymous
OH. Cool.

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