Question

Suppose the first term of a geometric sequence is multiplied by a nonzero constant, c. What happens to the following terms in the sequence? What happens to the sum of this geometric sequence? (This question has one right answer.) Give an example of a geometric sequence to illustrate your reasoning. (Many answers are possible.)

Answer 1

@jim_thompson5910

Answer 2

what did you get

Answer 3

the ratio would remain the same and the nonzero constant would be multiplied to the next term .... Thats all i got so far

Answer 4

does it say that you multiply c by the next term?

Answer 5

No but thats what you would do

Answer 6

yes but it doesn't explicitly tell you to

it just tells you to multiply the first term by c

Answer 7

to keep it a geometric sequence, yes you would multiply everything else by c

since they left that part out, I think they meant for it not to be a geometric sequence anymore

Answer 8

also if you multiply everything by c, then you are effectively multiplying the sum by c as well

but again, they left that part out

Answer 9

on purpose for me to say that :)

Answer 10

i guess it's implied that you multiply everything else by c

wish they would have explicitly said it though

Answer 11

how could i give an example of it?

Answer 12

start with any number you want (call it a)

multiply it with any other number you want (call it r)

then multiply this new term with r to get the next term

repeat again to get the next term

etc

Answer 13

So @jim_thompson5910 would \[a(r)^{1},a(r)^{2},a(r)^{3}\] be an example?

Answer 14

that's the basic form, yes

Answer 15

replace a and r with any numbers you want to get a more concrete example

Answer 16

whats another form?

Answer 17

ohhh ok thx :)

Answer 18

np