Question

Q4) Identify which of the following are geometric sequences and which are

Answer 1

Answer:

(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

$\frac{5}{25}$ = $\frac{1}{5}$ and $\frac{a_{3} }{a_{2} }$ = $\frac{1}{5}$

There is a common ratio r = $\frac{1}{5}$ , 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