anonymous
  • anonymous
1. Determine whether the sequence converges or diverges. If it converges, give the limit. 60, 10, 5/8 , 5/18 , ... Converges; 72 Converges; 0 Diverges Converges; -15540 2.) find an explicit rule for the nth term of the sequence. 1, 3, 9, 27, ... an = 1 • 3n + 1 an = 3 • 1n - 1 an = 1 • 3n - 1 an = 1 • 3n 3. Find an explicit rule for the nth term of the sequence. -5, -25, -125, -625, an = -5 • 5n an = 5 • -5n + 1 an = 5 • -5n an = -5 • 5n - 1
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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phi
  • phi
Your first sequence 60, 10, 5/8 , 5/18 , does not have a common ratio, so it is not a simple geometric sequence in other words to get from 60 to 10, multiply by 1/6 then from 10 multiply by 1/6 to get 10/6 = 5/3 but your third term is 5/8.
phi
  • phi
But each term is smaller the the one previous to it. So it is not diverging (growing larger and larger). So we can rule out choices about diverging and it is definitely not approaching 72 or -15540
anonymous
  • anonymous
@phi Converges; 0??

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phi
  • phi
If it continues getting smaller, (smaller and smaller fractions), it approaches 0
anonymous
  • anonymous
@phi what about number 3 and 2
phi
  • phi
For 2.) find an explicit rule for the nth term of the sequence. 1, 3, 9, 27, ... I would look at the differences: 3-1= 2 9-3= 6 27-9 = 18 that is not a constant difference. Then I would look at ratios: 3/1 = 3, 9/3 = 3; 27/9 = 3 that looks promising. To get from one term to the next, what do you multiply by ?
anonymous
  • anonymous
an = 1 • 3n - 1 @phi
phi
  • phi
You should put in ^ like this: 3^(n-1) other wise it looks like 3*n -1 which is different (and hard for me to figure out what you mean)
phi
  • phi
to figure out that rule I would like the number of the term, starting at 1 1 then the value 1 1 2 1*3 (I used the rule, multiply the previous term by 3) 3 1*3*3 4 1*3*3*3 if you know about exponents, when you multiply 3*3, you can write 3^2 and 3*3*3 is 3^3 so the table looks like this 1 1 2 1*3^1 3 1*3^2 4 1*3^3 now notice the exponent on the 3 is 1 less than the number of the term 1 1*3^(1-1) 2 1*3^(2-1) 3 1*3^(3-1) 4 1*3^(4-1) n 1*3^(n-1) for term n, this is the value
anonymous
  • anonymous
^^ @phi thank u so much what did u get for 3
phi
  • phi
3. Find an explicit rule for the nth term of the sequence. -5, -25, -125, -625, what do you multiply by to get the next term?
anonymous
  • anonymous
an = 5 • -5n + 1 @phi is it this one?
phi
  • phi
when n is 1 , using that rule what do you get? \[ 5 \cdot -5^{n+1} \] replace n with 1 and you get \[ 5 \cdot -5^2 \] which means \[ 5 \cdot - (5\cdot 5) = - 5 \cdot 5 \cdot 5 = -125 \] but we want -5 as the first term (when n=1)
anonymous
  • anonymous
a=-5 r=-25/-5=5 \[an=ar ^{n-1}\]
phi
  • phi
You should try to see how to do the problem (or just memorize the formula surji posted... but that tends to go in one ear and out the other if you don't understand what is going on)

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