0
The simplest rule that will generate the 4 terms, and the nth term is
Un = 2n2 + n + 3
Then Sn = Sum for k = 1 to n of (2k2 + k + 3)
= 2*sum(k2) + sum(k) + sum(3)
= 2*n*(n+1)*(2n+1)/6 + n*(n+1)/2 + 3*n
= (2n3 + 3n2 + n)/3 + (n2 + n)/2 + 3n
= (4n3 + 9n2 + 23n)/6
The simplest rule that will generate the 4 terms, and the nth term is
Un = 2n2 + n + 3
Then Sn = Sum for k = 1 to n of (2k2 + k + 3)
= 2*sum(k2) + sum(k) + sum(3)
= 2*n*(n+1)*(2n+1)/6 + n*(n+1)/2 + 3*n
= (2n3 + 3n2 + n)/3 + (n2 + n)/2 + 3n
= (4n3 + 9n2 + 23n)/6
The simplest rule that will generate the 4 terms, and the nth term is
Un = 2n2 + n + 3
Then Sn = Sum for k = 1 to n of (2k2 + k + 3)
= 2*sum(k2) + sum(k) + sum(3)
= 2*n*(n+1)*(2n+1)/6 + n*(n+1)/2 + 3*n
= (2n3 + 3n2 + n)/3 + (n2 + n)/2 + 3n
= (4n3 + 9n2 + 23n)/6
The simplest rule that will generate the 4 terms, and the nth term is
Un = 2n2 + n + 3
Then Sn = Sum for k = 1 to n of (2k2 + k + 3)
= 2*sum(k2) + sum(k) + sum(3)
= 2*n*(n+1)*(2n+1)/6 + n*(n+1)/2 + 3*n
= (2n3 + 3n2 + n)/3 + (n2 + n)/2 + 3n
= (4n3 + 9n2 + 23n)/6
What else can I help you with?
What is the formula for the nth Term of these sequences 13 21 29 37 45 ...?
nth term = 5 +8n
What is the formula for the nth term of this sequence -1-7-13-19-25?
The nth term is: 5-6n
What is the nth term of 10 13 16 19?
The nth term is 3n+7 and so the next number will be 22
What is the Nth term of 4 7 10 13...?
The nth term is: 3n+1 and so the next number will be 16
What is the nth term of 3 8 13 18 23?
Un = 5n - 2
What is the nth term for the sequence 1 6 13 22 33?
The given sequence is 1, 6, 13, 22, 33. To find the nth term, we can observe that the differences between consecutive terms are 5, 7, 9, and 11, which indicates that the sequence is quadratic. The nth term can be expressed as ( a_n = n^2 + n ), where ( a_n ) is the nth term of the sequence. Thus, the formula for the nth term is ( a_n = n^2 + n ).
What is the nth term for 0 1 1 2 3 5 8 13?
This is the Fibonacci sequence, where the number is the sum of the two preceding numbers. The nth term is the (n-1)th term added to (n-2)th term
What is the nth term for 4 13 28 49 76?
To find the nth term of the sequence 4, 13, 28, 49, 76, we first identify the differences between consecutive terms: 9, 15, 21, 27. The second differences, which are constant at 6 (6, 6, 6), suggest that the sequence is quadratic. The nth term can be expressed as ( an^2 + bn + c ). By solving the equations based on the first few terms, we find the nth term is ( n^2 + 3n ).
What is the nth term rule of the linear sequence of -9-5-137?
To find the nth term of the linear sequence -9, -5, -1, we first identify the common difference between the terms. The difference between consecutive terms is 4. The first term (a) is -9, so the nth term can be expressed as ( a_n = -9 + (n-1) \cdot 4 ), which simplifies to ( a_n = 4n - 13 ).
What is the nth term for the sequence -2 1 6 13 22 33?
The given sequence is -2, 1, 6, 13, 22, 33. To find the nth term, we observe that the differences between consecutive terms are increasing by 2 (3, 5, 7, 9). This indicates a quadratic pattern, and the nth term can be expressed as ( a_n = n^2 + n - 2 ). Thus, the nth term of the sequence is ( a_n = n^2 + n - 2 ).
What is the formula for the nth Term of these sequences 13 21 29 37 45 ...?
nth term = 5 +8n
What is the formula for the nth term of this sequence -1-7-13-19-25?
The nth term is: 5-6n
What is the nth term of 10 13 16 19?
The nth term is 3n+7 and so the next number will be 22
What is the Nth term of 4 7 10 13...?
The nth term is: 3n+1 and so the next number will be 16
What is the nth term for 5 10 19 32 49 nth term?
To find the nth term of this sequence, we first need to identify the pattern. The differences between consecutive terms are 5, 9, 13, 17, and so on. These are increasing by 4 each time. This means that the nth term can be calculated using the formula n^2 + 4n + 1. So, the nth term for the sequence 5, 10, 19, 32, 49 is n^2 + 4n + 1.
How did you get the answer for the nth term of sequence 3 8 13 18?
To find the nth term of the sequence 3, 8, 13, 18, I first identified the pattern in the differences between consecutive terms: 5, 5, 5. Since these differences are constant, the sequence is linear. The nth term can be expressed in the form ( a_n = an + b ). By using the first term (3) and the common difference (5), I derived the formula: ( a_n = 5n - 2 ).
What is the nth term of 3 8 13 18 23?
Un = 5n - 2
