Q4) Identify which of the following are geometric sequences and which are not
(i) 2, 6, 18, 54
(ii) 25,5, 1,
(iii) 1, 4, 9, 16

(i) and (ii)

Step-by-step explanation:

For a sequence to be geometric then the ratio r between consecutive terms must be common.

(1)

2, 6, 18, 54

6 ÷ 2 = 3

18 ÷ 6 = 3

54 ÷ 18 = 3

Here there is a common ratio r = 3 , then sequence is geometric

(ii)

25, 5, 1

= and =

There is a common ratio r = , then sequence is geometric

(iii)

1, 4, 9, 16

4 ÷ 1 = 4

9 ÷ 4 = 2.25

16 ÷ 9 = 1.777..

There is no common ratio, then sequence is not geometric

Integers may be positive or negative. They are whole numbers. 
Rational expression is a fraction wherein a numerator and/or a denominator are polynomials.

Division of integers is like dividing whole numbers. You only have to take not of the positive or negative sign of each integer to determine the sign of the quotient.

Division of rational expression:
1) flip and multiply
2) factor the numerator and denominator
3) cancel duplicate factors and simplify.