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anonymous
 one year ago
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
anonymous
 one year ago
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. 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
 one year ago
Best ResponseYou've already chosen the best response.0Yeah so like the number is 3 and 8*3 = 24 and 24*3 = 72 and 72*3= 216 and so on.. @elite.weeaboo

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0216*3= 648, 648*3= 1944, 1944*3= 5832

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wait until idku is done typing. I could be wrong.

idku
 one year ago
Best ResponseYou've already chosen the best response.0Oh, no it is correct, i was just going to make a definitional [ost.

idku
 one year ago
Best ResponseYou've already chosen the best response.0just 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.... \(a_1 \times r^{n1} = a_n \)

idku
 one year ago
Best ResponseYou've already chosen the best response.0So if you wanted to find 1000th term of your sequence, you would go: \(a_1 \times r^{n1} = a_n \) \(a_1 \times r^{10001} = a_{1000} \) your first term is 8, so: \((8) \times r^{10001} = a_{1000} \) your common ratio is 3: \((8) \times (3)^{10001} = a_{1000} \) \(\color{blue}{(8) \times (3)^{999} = a_{1000}} \)
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