Question

Find the common ratio for this geometric sequence.

Answer 1

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 ,

$\rm\implies Series = 72 , 12 , 2 , \dfrac{1}{3},\dfrac{1}{18}$

We can find the common ratio by dividing the consecutive terms , As ,

$\rm\implies Common \ Ratio (r) = \dfrac{ n \ th \ term }{ ( n - 1)th \ term }$

Substitute the respective values ,

$\rm\implies Common \ Ratio (r) = \dfrac{ 12 }{ 72 }$

Simplify by dividing the term in RHS ,

$\rm\implies \boxed{\blue{\rm Common \ Ratio (r) = \dfrac{ 1 }{ 6 } }}$

Hence the common ratio is 1/6 .