Answer:
2/3
Step-by-step explanation:
2nd term = 2/5
5th term = 16/135
Nth term for any series is given by [tex]a r^n-1[/tex]
where a is the forst term
r is the common ratio
for 2nd term
[tex]2nd \ term = ar^n-1 = 2/5\\2nd \ term = ar^2-1 = 2/5\\2nd \ term = ar= 2/5\\[/tex]
for 5th term
[tex]5th \ term = ar^5-1 = 16/135\\\\5th \ term = ar^4 = 16/135\\[/tex]
Since we have to eliminate a and find r .
we can divide 5th term by second term
then we get the following equation
[tex]2nd term/ 5th \ term = ar/ar^4 = (2/5) / (16/135)\\=>1/r^3 = 2*135/5*16 \\=>1/r^3 = 27/8\\=>1/r = \sqrt[3]{27/8} \\=> 1/r = 3/2\\=> r = 2/3[/tex]
\
Thus, common ratio is 2/3.
