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

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plohrr
 10 months ago
Best ResponseYou've already chosen the best response.0@SolomonZelman @jim_thompson5910

jim_thompson5910
 10 months ago
Best ResponseYou've already chosen the best response.15r = 10 r = ???

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

plohrr
 10 months ago
Best ResponseYou've already chosen the best response.05n = 5 x (2) n1 5n = 10 n1 What do i do from here

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.2no 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)

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

myininaya
 10 months ago
Best 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

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.2again 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

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.2you 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

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

plohrr
 10 months ago
Best ResponseYou've already chosen the best response.0Does the 5 not go where the n is

jim_thompson5910
 10 months ago
Best ResponseYou've already chosen the best response.15 goes where 'a' is but \(\Large a_n\) is NOT the same as just 'a'

jim_thompson5910
 10 months ago
Best ResponseYou've already chosen the best response.1If 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

jim_thompson5910
 10 months ago
Best ResponseYou've already chosen the best response.1The 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 > \(\Large a_n = a_{17}\)

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

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

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

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

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.2r 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

myininaya
 10 months ago
Best ResponseYou've already chosen the best response.2also this was already determined way above when joe was working with you
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