Question

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

Answer 1

if i remember correctly there is not one

Answer 2

see if i can remember the proof

Answer 3

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

Answer 4

but it can be a combination

Answer 5

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

Answer 6

can i have my dirty martini now?

Answer 7

^correct

Answer 8

uh not the martini lol

Answer 9

actually trying to find the n th term

Answer 10

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

Answer 11

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

Answer 12

got it yes?

Answer 13

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

Answer 14

ahh you want the eleventh term maybe

Answer 15

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

Answer 16

yes want the 11th term

Answer 17

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

Answer 18

(calculator)

Answer 19

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

Answer 20

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

Answer 21

sure name it

Answer 22

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

Answer 23

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

Answer 24

instructions read find the term, yes geometric

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

*formula

Answer 30

why is the answer a number and not a letter
]

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

thank you, just figured out y as well

Answer 35

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

Answer 36

what kind of math is this?

Answer 37

honors geometry

Answer 38

just transferd into the class and missed the first 2 lessons

Answer 39

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