Question

2,5, 25/2, ...
find the 10th term

Answer 1

The
`10^(th)` term of the given sequence

`t_(10) = (5^(9) )/(2^(8) )`

Explanation:

Step(i):-

Given sequence 2 , 5,
`(25)/(2)`

First term a = 2

The difference of given geometric sequence

`d = (r_(2) )/(r_(1) ) = (5)/(2)`

Step(ii):-

The
`n^(th)` term of the given sequence

`t_(n) = ar^(n-1)`

The
`10^(th)` term of the given sequence

`t_(10) = (2)((5)/(2) )^(10-1)`

`t_(10) = (2)((5)/(2) )^(9)= (5^(9) )/(2^(8) )`