what should be the next term in this sequence 5832, 9261, 13824, 19683
Answers
27000 is the next term in the series.
5832, 9261, 13824, 19683 , 27000
Step-by-step explanation:
Given:
5832, 9261, 13824, 19683
To find:
The next term in the series.
Solution:
This series is a numerical sequence in which the numbers are arranged orderly and make a sequence.
The pattern is (x₁,x₂,x₃,x₄,x₅) are the numbers in the series thus x₁=18³, 21³⇒x₂, 24³⇒x₃, 27³⇒x₄, 30³⇒x₅.
The pattern of this series is the cubic terms of (18,21,24,27,30). The pattern is thus arranged orderly with the addition of 3 periodically.
The first number 5832 is obtained by a cubic term of 18. Thus we get x₁ as the first number.
5832 ⇒x₁
⇒18×18×18
⇒18³=5832
The second number 9261 is obtained by a cubic term of 21. Thus we get x₅ the second number. The second cubic term will be 18 in addition with 3 we get 21.
9261⇒x₂
⇒21 ×21 ×21
⇒21³=9261
The third number 13824 is obtained by a cubic term of 24. Thus we get x₅ the third number. The third cubic term will be 21 in addition to 3 we get 24.
13824⇒x₃
⇒24 ×24 ×24
⇒24³=13824
The fourth number 19683 is obtained by a cubic term of 27. Thus we get x₄ the fourth number. The fourth cubic term will be 24 in addition with 3 we get 27.
19683⇒x₄
⇒27 ×27× 27
⇒27³=19683
The fifth number 30000 is obtained by a cubic term of 30. Thus we get x₅ the fifth number. The fifth cubic term will be 27 in addition to 3 we get 30.
The next number in the series is
30000⇒x₅
⇒30 ×30 ×30
⇒30³
⇒27000
Hence,
The next number in the series is 27000.
5832,9261, 13824, 19683, 27000