Write the next term of sequence,and then write the rule for the nth term.
1)1,8,27,64,....125
the nth is n
2) 3,8,15, 24,.....35
the nth is
Can you help me and correct ? thank you
1) looks like you are dealing with the cubes
so term(n) = n^3
2) did you notice that each term is one less than a perfect square?
e.g.
3 = 2^2 - 1 --term(1)
8 = 3^2 -1 -- term(2)
15 = 4^2 -1
24 = 5^2 - 1
35 = 6^2 - 1
so term(n) = (n+1)^2 -1
Sure! Let's solve these two questions step by step:
1) The given sequence is 1, 8, 27, 64, ....
To find the next term, we can observe that each term is the cube of the respective natural numbers: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64.
Hence, the next term would be 5^3 = 125.
The rule for the nth term would be tn = n^3.
2) The given sequence is 3, 8, 15, 24, ....
To find the next term, we can observe that the difference between consecutive terms is increasing by 2 each time: 8 - 3 = 5, 15 - 8 = 7, 24 - 15 = 9.
Hence, the difference between the next term and the last term would be 9 + 2 = 11.
Thus, the next term would be 24 + 11 = 35.
The rule for the nth term in this case would be tn = n^2 + 2n + 1.
So, the correct next terms and rules for the given sequences are:
1) Next term: 125, Rule: tn = n^3.
2) Next term: 35, Rule: tn = n^2 + 2n + 1.