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

Question

anonymous · Answer

if i remember correctly there is not one

anonymous · Answer

see if i can remember the proof

anonymous · Answer

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

anonymous · Answer

but it can be a combination

anonymous · Answer

your sequence above is 
$$2^n-1$$for 
$$n=1,2,3,...$$

anonymous · Answer

can i have my dirty martini now?

anonymous · Answer

^correct

anonymous · Answer

uh not the martini lol

anonymous · Answer

actually trying to find the n th term

anonymous · Answer

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

anonymous · Answer

first term is 
$$2^1-1=1$$ second term is 
$$2^2-1=3$$third term is 
$$2^3-1=7$$ nth term is 
$$2^n-1$$

anonymous · Answer

got it yes?

anonymous · Answer

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

anonymous · Answer

ahh you want the eleventh term maybe

anonymous · Answer

that would be 
$$2^{11}-1$$

anonymous · Answer

yes want the 11th term

anonymous · Answer

which is 
$$2^{11}-1=2047$$

anonymous · Answer

(calculator)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

sure name it

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

instructions read find the term, yes geometric

anonymous · Answer

because it looks like it should be 
$$3,6,9,12, 15,18,...$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

*formula

anonymous · Answer

why is the answer a number and not a letter
]

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

thank you, just figured out y as well

anonymous · Answer

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

anonymous · Answer

what kind of math is this?

anonymous · Answer

honors geometry

anonymous · Answer

just transferd into the class and missed the first 2 lessons

anonymous · Answer

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