Question

How do you know if a sequence is a geometric sequence? Please explain.

I am trying to find r for this sequence and whether it is or not a geometric sequence.
1/2, 2, 8, 32, ...

Answer 1

help

Answer 2

\[\huge\rm r= \frac{ a_2 }{ a_1 } , \frac{ a_4}{ a_3 }\]
to find ratio
divide next term by previous one
you a_4/ a_3 = ?
a_2 /a_1 = ?

Answer 3

wait how do i know if the given sequence is geometric?

Answer 4

my teacher said times by common factor i think

Answer 5

yea
first divide terms
if you get same number then that's mean sequence is increasing by same value so it's geometric if u get different number then it's not a geometric sequence

Answer 6

what or how do I know what to divide the terms by?

Answer 7

Am I suppose to divide by the previous terms

Answer 8

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
\[\huge\rm r= \frac{ a_2 }{ a_1 } , \frac{ a_4}{ a_3 }\]
to find ratio
divide next term by previous one
you a_4/ a_3 = ?
a_2 /a_1 = ?
\(\color{blue}{\text{End of Quote}}\)
here a represent terms
a_2 = 2nd term
a_3 = 3rd term
so on

Answer 9

yes right

Answer 10

ohh, common ratio! I get it now

Answer 11

thanks

Answer 12

yep right so it's geometric or nope ?

Answer 13

yes

Answer 14

common ratio is 4, in other words, ratio is 4

Answer 15

yes right so if you divide a_4 by 3rd term you would get same answer which is 4
so it's a geometric sequence