Question : Directions: In the following question a series is given, with one or more numbers missing. Choose the correct alternative from the given ones that will complete the series.
0.2, 0.16, 0.072, 0.0256, ?
Option 1: 0.0016
Option 2: 0.004
Option 3: 0.00512
Option 4: 0.008
Correct Answer: 0.008
Solution :
Given:
0.2, 0.16, 0.072, 0.0256, ?
Each term in the series is formed by multiplying 2, 2 raise to power natural numbers (which will increase in each term by 1), and a square of consecutive natural numbers. The resultant will then be divided by 10, 100, 1000, and so on.
2 = (2 × 2
0
× 1
2
) ÷ 10
0.16 = (2 × 2
1
× 2
2
) ÷ 100
0.072 = (2 × 2
2
× 3
2
) ÷ 1000
0.0256 = (2 × 2
3
× 4
2
) ÷ 10000
Thus, the next number will be (2 × 2 4 × 5 2 ) ÷ 100000 = 800 ÷ 100000 = 0.008
So, 0.008 is the missing term of the given series. Hence, the fourth option is correct.