Question

Is it possible for a sequence to be both an arithmetic sequence and a geometric sequence? Explain

Answer 1

try it and see
see if you can make a geometric sequence \(a,ar,ar^2,...\) that is also arithmetic i.e. \(a, a+d, a+2d,...\)

Answer 2

@satellite73 i dont think i can do that

Answer 3

no you can't

Answer 4

0

Answer 5

ok...

Answer 6

so you cant do what the equations said its is not possible?

Answer 7

What about constant sequence?

Ex: \(2,2,2,2,2,2,2,2\cdots\)

Answer 8

What if we let \(r=1\) and \(d=0\)?

Answer 9

@satellite73

Answer 10

Im not really good at this

Answer 11

i guess constants :)

Answer 12

or this would be a weird one but...
infinities?

Answer 13

what you are being told is that if a sequence is both geometric and arithmetic then it is a constant, i.e. \(r=1\) and \(d=0\)
we can probably prove that if you like

Answer 14

it is a pretty standard proof, i can walk you through it if you like

Answer 15

yes plz