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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 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 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.
What is the nth term of 3 8 13 18 23?
Un = 5n - 2
What is the nth term for the sequences 7 13 19 25?
The nth term is 6n+1 and so the next term will be 31
What is the nth term 9 13 17 21?
It is 4n+5 and so the next term will be 25
what is the nth term of 13, 16, 19, 22?
The nth term of an arithmetic sequence is given by. an = a + (n – 1)d. The number d is called the common difference because any two consecutive terms of an. arithmetic sequence differ by d, and it is found by subtracting any pair of terms an and. an+1.
What is the nth term of the sequence 13 17 21 25 29?
The given sequence is an arithmetic sequence where each term increases by 4. The first term (a) is 13, and the common difference (d) is 4. The nth term can be found using the formula: ( a_n = a + (n-1)d ). Therefore, the nth term is ( a_n = 13 + (n-1) \cdot 4 = 4n + 9 ).
What is the nth term for 1 7 13 19?
The given sequence is an arithmetic sequence with a common difference of 6. To find the nth term of this sequence, we can use the following formula: nth term = first term + (n - 1) x common difference where n is the position of the term we want to find. In this sequence, the first term is 1 and the common difference is 6. Substituting these values into the formula, we get: nth term = 1 + (n - 1) x 6 nth term = 1 + 6n - 6 nth term = 6n - 5 Therefore, the nth term of the sequence 1, 7, 13, 19 is given by the formula 6n - 5.
