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 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0@SolomonZelman @jim_thompson5910

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

jim_thompson5910
 8 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
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0Ok, so how do i set up this equation

myininaya
 8 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
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0So how do i set up the equation ? im confused

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

jim_thompson5910
 8 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
 8 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
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.0Ok, so you leave the an as it is

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

plohrr
 8 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
 8 months ago
Best ResponseYou've already chosen the best response.2how do you get 15 for r?

myininaya
 8 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
 8 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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