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plohrr
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what are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of 10
 one month ago
 one month ago
plohrr Group Title
what are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of 10
 one month ago
 one month ago

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plohrr Group TitleBest ResponseYou've already chosen the best response.0
@Hero @ganeshie8
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
@SolomonZelman @jim_thompson5910
 one month ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
5r = 10 r = ???
 one month ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
First Term: a = 5 Common Ratio: r = 2 Plug those into \[\Large a_{n} = a*(r)^{n1}\] to get the general nth term formula
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
5n = 5 x (2) n1 5n = 10 n1 What do i do from here
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
no a_n symbolizes the n term of the sequence a_n and a are different values also we don't have (ar)^(n1) we just have that the r is to the (n1)
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
Ok, so how do i set up this equation
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[a_n=a \cdot r^{n1}\] just replace the a with 5 and replace the r with 2 like jim said
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
5n = 10^n1 ?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
again a_n and a are different values a_n is a variable by itself you can't multiply a and r because r has an exponent
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
5_n = 5 x 2^n1
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
you cannot replace a_n with 5_n this makes no sense let me show you how this formula is come up with so maybe you understand better {a_n} is a sequence of numbers those numbers are a_1=5 a_2=5(2)=10 a_3=5(2)(2)=5(2)^2=20 a_4=5(2)(2)(2)=5(2)^3=40 a_5=5(2)(2)(2)(2)=5(2)^4=80 ... therefore a_n=5(2)(2)(2)(2)(2)(2)...(2)= (by the way that is a (n1) amount of (2)) I put a (n1) amount of (2) because looking at a_1 we have (2)^0=(2)^(11) looking at a_2 we have (2)^1=(2)^(21) looking at a_3 we have (2)^2=(2)^(31) it is always one less than where the number is in the sequence
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
So how do i set up the equation ? im confused
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
Does the 5 not go where the n is
 one month ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
5 goes where 'a' is but \(\Large a_n\) is NOT the same as just 'a'
 one month ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
If it confuses you, think of it as \[\Large T = a*(r)^{n1}\] T = nth term a = first term r = common ratio n = positive whole number (used to identify which term you're dealing with) example: n = 3 > 3rd term
 one month ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
The notation \(\Large a_n\) is used for sequences because the 'n' changes to a positive whole number to indicate a certain term example: 17th term > n = 17 > \(\Large a_n = a_{17}\)
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
Ok, so you leave the an as it is
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Yep it is a formula for the nth term in the sequence
 one month ago

plohrr Group TitleBest ResponseYou've already chosen the best response.0
So it is an = 5 (15)^n1; all integers where n less than or equal to 1
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
how do you get 15 for r?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
r symbolizes the geometric ratio to find r all you have to do is evaluate a_2/a_1 or take any two consecutive numbers in the sequence and put the 2 nd term of those numbers over the 1st term of those numbers
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
also this was already determined way above when joe was working with you
 one month ago
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