OpenStudy (anonymous):

how do you find the indicated term of a sequence that is both Arithmetic and geometric? for example: 1,3,7,15,31,63

6 years ago
OpenStudy (anonymous):

if i remember correctly there is not one

6 years ago
OpenStudy (anonymous):

see if i can remember the proof

6 years ago
OpenStudy (anonymous):

u find a relationship between the sequence but it cannot be arithmetic or geometric

6 years ago
OpenStudy (anonymous):

but it can be a combination

6 years ago
OpenStudy (anonymous):

your sequence above is \[2^n-1\]for \[n=1,2,3,...\]

6 years ago
OpenStudy (anonymous):

can i have my dirty martini now?

6 years ago
OpenStudy (anonymous):

^correct

6 years ago
OpenStudy (anonymous):

uh not the martini lol

6 years ago
OpenStudy (anonymous):

actually trying to find the n th term

6 years ago
OpenStudy (anonymous):

i wrote the nth term. it is \[2^n-1\] the "nth term" naturally has an "n" in it yes?

6 years ago
OpenStudy (anonymous):

first term is \[2^1-1=1\] second term is \[2^2-1=3\]third term is \[2^3-1=7\] nth term is \[2^n-1\]

6 years ago
OpenStudy (anonymous):

got it yes?

6 years ago
OpenStudy (anonymous):

the problem reads 1,3,7,15,31,63....,a11

6 years ago
OpenStudy (anonymous):

ahh you want the eleventh term maybe

6 years ago
OpenStudy (anonymous):

that would be \[2^{11}-1\]

6 years ago
OpenStudy (anonymous):

yes want the 11th term

6 years ago
OpenStudy (anonymous):

which is \[2^{11}-1=2047\]

6 years ago
OpenStudy (anonymous):

(calculator)

6 years ago
OpenStudy (anonymous):

using the same problem what if I wanted to find the 5th term

6 years ago
OpenStudy (anonymous):

nevermind, i got it. can I give you 1 more problem

6 years ago
OpenStudy (anonymous):

sure name it

6 years ago
OpenStudy (anonymous):

a,6,c,12,e,18 ...., a25

6 years ago
OpenStudy (anonymous):

there must be some sort of instructions yes? is it geometric?

6 years ago
OpenStudy (anonymous):

instructions read find the term, yes geometric

6 years ago
OpenStudy (anonymous):

because it looks like it should be \[3,6,9,12, 15,18,...\]

6 years ago
OpenStudy (anonymous):

and that is not geometric, it is arithmetic. you are adding 3 to one term to get the next

6 years ago
OpenStudy (anonymous):

ok, do the 25th term will be a letter, right? how do i determine the lettter

6 years ago
OpenStudy (anonymous):

so the formal would be \[a_n=3n\] and therefore \[a_{25}=75\]

6 years ago
OpenStudy (anonymous):

*formula

6 years ago
OpenStudy (anonymous):

why is the answer a number and not a letter ]

6 years ago
OpenStudy (anonymous):

oh i thought the letters represented numbers you were not given. maybe i am wrong

6 years ago
OpenStudy (anonymous):

if so i guess it is the 25th letter of the alphabet, which is y

6 years ago
OpenStudy (anonymous):

no I think you are right. the letters are numbers not given

6 years ago
OpenStudy (anonymous):

thank you, just figured out y as well

6 years ago
OpenStudy (anonymous):

well i am no sure, but it is either y or 75

6 years ago
OpenStudy (anonymous):

what kind of math is this?

6 years ago
OpenStudy (anonymous):

honors geometry

6 years ago
OpenStudy (anonymous):

just transferd into the class and missed the first 2 lessons

6 years ago
OpenStudy (anonymous):

what if the ratio is not constant, example: 1,3,6,10,15,21... a30

6 years ago