Answer:
The geometric sequences are:
16 , -8 , 4 , -2 , 1 ⇒ 2nd
-15 , -18 , -21.6 , -25.92 , -31.104, ........ ⇒ 3rd
625 , 125 , 25 , 5 , 1 , ........ ⇒ 5th
Step-by-step explanation:
In the geometric sequence there is a constant ratio between each two consecutive terms
Let us find which sequence has a constant ratio between its consecutive terms
-2 , -4 , -6 , -8 , -10
∵ -4 ÷ -2 = 2
∵ -6 ÷ -4 = 1.5
- No constant ratio between the consecutive terms
∴ The sequence is not geometric
16 , -8 , 4 , -2 , 1
∵ -8 ÷ 16 = -0.5
∵ 4 ÷ -8 = -0.5
∵ -2 ÷ 4 = -0.5
∵ 1 ÷ -2 = -0.5
- There is a constant ratio -0.5 between the consecutive terms
∴ The sequence is geometric
-15 , -18 , -21.6 , -25.92 , -31.104, ........
∵ -18 ÷ -15 = 1.2
∵ -21.6 ÷ -18 = 1.2
∵ -25.92 ÷ -21.6 = 1.2
∵ 31.104 ÷ 25.92 = 1.2
- There is a constant ratio 1.2 between the consecutive terms
∴ The sequence is geometric
4 , 10.5 , 17 , 23.5 , 30, ......
∵ 10.5 ÷ 4 = 2.625
∵ 17 ÷ 10.5 = 1.619047619
- No constant ratio between the consecutive terms
∴ The sequence is not geometric
625 , 125 , 25 , 5 , 1 , ........
∵ 125 ÷ 625 = 0.2
∵ 25 ÷ 125 = 0.2
∵ 5 ÷ 25 = 0.2
∵ 1 ÷ 5 = 0.2
- There is a constant ratio 0.2 between the consecutive terms
∴ The sequence is geometric
⇒⇒⇒⇒ rule (2)
⇒⇒⇒⇒ rule (1) and rule (2)
⇒⇒⇒⇒ rule (3)