Question

6th term 25,75,225,675,.... is it arithmetic or geometric. what's the explicit equation and the given term​

Answer 1

see explanation

Explanation:

There is a common ratio r between consecutive terms, that is

`(a_(2) )/(a_(1) )` =
`(75)/(25)` = 3

`(a_(3) )/(a_(2) )` =
`(225)/(75)` = 3

`(a_(4) )/(a_(3) )` =
`(675)/(225)` = 3

This indicates the sequence is geometric with explicit formula

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 25 and r = 3 , then

a₆ = 25 ×
`3^(5)` = 25 × 243 = 6075