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anonymous
 one year ago
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
anonymous
 one year ago
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

This Question is Closed

phi
 one year ago
Best ResponseYou've already chosen the best response.0Your 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
 one year ago
Best ResponseYou've already chosen the best response.0But 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

phi
 one year ago
Best ResponseYou've already chosen the best response.0If it continues getting smaller, (smaller and smaller fractions), it approaches 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@phi what about number 3 and 2

phi
 one year ago
Best ResponseYou've already chosen the best response.0For 2.) find an explicit rule for the nth term of the sequence. 1, 3, 9, 27, ... I would look at the differences: 31= 2 93= 6 279 = 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 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.0You should put in ^ like this: 3^(n1) other wise it looks like 3*n 1 which is different (and hard for me to figure out what you mean)

phi
 one year ago
Best ResponseYou've already chosen the best response.0to 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^(11) 2 1*3^(21) 3 1*3^(31) 4 1*3^(41) n 1*3^(n1) for term n, this is the value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0^^ @phi thank u so much what did u get for 3

phi
 one year ago
Best ResponseYou've already chosen the best response.03. 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
 one year ago
Best ResponseYou've already chosen the best response.0an = 5 5n + 1 @phi is it this one?

phi
 one year ago
Best ResponseYou've already chosen the best response.0when 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
 one year ago
Best ResponseYou've already chosen the best response.0a=5 r=25/5=5 \[an=ar ^{n1}\]

phi
 one year ago
Best ResponseYou've already chosen the best response.0You 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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