30,48,68,90,.... What is the resoective series number after 90
Answers
Number after 90 is 114 in series 30,48,68,90,..
Tₙ₊₁ = Tₙ + 16 + 2n where n≥ 1 , n∈ Z and T₁ = 30
Given:
- Series 30,48,68,90,..
To Find:
Number after 90
Solution:
Understand the series:
30 48 68 90 114
18 20 22 24
2 2 2
2nd Difference is constant here Hence , Difference between two consecutive terms is increasing by 2
Hence, number after 90 is 114
30 + 18 = 48
48 + 20 = 68
68 + 22 = 90
90 + 24 = 114
Another way to understand the series
30
30 + 16 + 2 x 1 = 48
48 + 16 + 2 x 2 = 68
68 + 16 + 2 x 3 = 90
90 + 16 + 2 x 4 = 114
Tₙ₊₁ = Tₙ + 16 + 2n where n≥ 1 , n∈ Z and T₁ = 30
Answer:
The next number of the series is 112.
Step-by-step explanation:
Recursive series:
A constant-recursive sequence is an infinite number series in mathematics and theoretical computer science where each number is identical to a fixed linear combination of one or more of its immediate predecessors.
Given series is 30,48,68,90,....
Each term of the series follows a rule that is known as recursive.
30 48 68 90
First difference 18 20 22
Second difference 2 2
Therefore,
The second term: 48 = 30 + 18 = 30 + 9×2
Third term: 68 = 48 +20 = 48 + 10×2
Fourth term: 90 = 68 + 22 = 68 + 11×2
The recursive rule: Tn₊1 = Tn + 2(7+ n)
Where n is the number of terms.
The fifth term is T₅ = T₄ + 2(7+ 5)
= 90 + 2×12
= 90 + 24
= 114.
To learn more about recursive sequence, click on the below link:
https://brainly.in/question/4585599
https://brainly.in/question/5962241
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