write four more rational numbers of each of the following patterns -1/4'-2/8'-3/12
Answers
(-1 × 1)/(4 × 1), (-1 × 2)/(4 × 2) , (-1 × 3)/(4 × 3) …
Next four rational numbers in the same pattern,
(-1 × 4)/(4 × 4), (-1 × 5)/(4 × 5) , (-1 × 6)/(4 × 6) , (-1 × 7)/(4 × 7)
Therefore, the numbers are -4/16 , -5/20 , -6/24 , -7/28 ⋯
Given:
A series of numbers -1/4, -2/8, -3/12.
To Find:
The next four terms of the given series.
Solution:
The given problem can be solved by developing a common logic between every term.
1. The given series is -1/4, -2/8, -3/12.
2. The second term is obtained using the logic,
=> -2/8 = - (first term numerator +1)/(first term denominator +4),
3. The third term is obtained using the logic,
=> -3/12 = - (second term numerator +1)/(second term denominator +4),
4. Similarly the next rational numbers can be found using the same logic,
=> Fourth term = - (3+1)/(12+4) = -4/16,
=> Fifth term = -(4+1)/(16+4) = -5/20,
=> Sixth term = -(5+1)/(20+4) = -6/24,
=> Seventh term = -(6+1)/(24+4) = -7/28.
Therefore, the next four terms of the series are -4/16, -5/20, -6/24, -7/28.