7
It appears to be -6
The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.
t(n) = 12*n + 5
Well, honey, looks like we've got ourselves an arithmetic sequence here with a common difference of 7. So, to find the nth term, we use the formula a_n = a_1 + (n-1)d. Plug in the values a_1 = 12, d = 7, and n to get the nth term. Math doesn't have to be a drag, darling!
The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7.
It appears to be -6
-13
yes, d = 7
The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.
t(n) = 12*n + 5
Well, honey, looks like we've got ourselves an arithmetic sequence here with a common difference of 7. So, to find the nth term, we use the formula a_n = a_1 + (n-1)d. Plug in the values a_1 = 12, d = 7, and n to get the nth term. Math doesn't have to be a drag, darling!
The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7.
No, geometric, common ratio 2
The sequence 216 12 23 is neither arithmetic nor geometric.
To find the value of the nth term in an arithmetic sequence, you can use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference between terms. In this sequence, the first term (a_1 = 12) and the common difference (d = -6 - 0 = -6). So, the formula becomes (a_n = 12 + (n-1)(-6)). Simplifying this gives (a_n = 12 - 6n + 6). Therefore, the value of the nth term in this arithmetic sequence is (a_n = 18 - 6n).
The explicit formula for an arithmetic sequence is given by an = a1 + (n-1)d, where a1 is the first term and d is the common difference. In this case, the first term a1 is 16, and the common difference d is 4. Therefore, the explicit formula for the arithmetic sequence is an = 16 + 4(n-1) = 4n + 12.
It is neither.