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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
 4 months ago
 4 months 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
 4 months ago
 4 months ago

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
5r = 10 r = ???
 4 months 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
 4 months 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
 4 months 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)
 4 months ago

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

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

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

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

plohrr Group TitleBest ResponseYou've already chosen the best response.0
Does the 5 not go where the n is
 4 months 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'
 4 months 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
 4 months 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 > \(\Large a_n = a_{17}\)
 4 months ago

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

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

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