Answer:
1/6
Step-by-step explanation:
We need to find the common ratio for the given Geometric Series . We know that ,
Geometric Series:- When a common number is multiplied to each term to obtain the next term of the Series is called Geometric Series .
Common Ratio :- The number which is multiplied to obtain the next term of the series .
Here the given series is ,
[tex]\rm\implies Series = 72 , 12 , 2 , \dfrac{1}{3},\dfrac{1}{18} [/tex]
We can find the common ratio by dividing the consecutive terms , As ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ n \ th \ term }{ ( n - 1)th \ term } [/tex]
Substitute the respective values ,
[tex]\rm\implies Common \ Ratio (r) = \dfrac{ 12 }{ 72 } [/tex]
Simplify by dividing the term in RHS ,
[tex]\rm\implies \boxed{\blue{\rm Common \ Ratio (r) = \dfrac{ 1 }{ 6 } }}[/tex]
Hence the common ratio is 1/6 .
