Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

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

$\frac{a_{2} }{a_{1} }$ = $\frac{75}{25}$ = 3

$\frac{a_{3} }{a_{2} }$ = $\frac{225}{75}$ = 3

$\frac{a_{4} }{a_{3} }$ = $\frac{675}{225}$ = 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