Question

Please Please PLease help

Answer 1

2/3

Explanation:

2nd term = 2/5

5th term = 16/135

Nth term for any series is given by
`a r^n-1`

where a is the forst term

r is the common ratio

for 2nd term

`2nd \ term = ar^n-1 = 2/5\\2nd \ term = ar^2-1 = 2/5\\2nd \ term = ar= 2/5\\`

for 5th term

`5th \ term = ar^5-1 = 16/135\\\\5th \ term = ar^4 = 16/135\\`

Since we have to eliminate a and find r .

we can divide 5th term by second term

then we get the following equation

`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`

\

Thus, common ratio is 2/3.