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.
12, 6, 0, -6, ...
It appears to be -6
8 + 4n
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 sequence 216 12 23 is neither arithmetic nor geometric.
12, 6, 0, -6, ...
It appears to be -6
8 + 4n
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 sequence 216 12 23 is neither arithmetic nor geometric.
No, the sequence 3, 6, 12, 24 is not an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant. Here, the differences are 3 (6-3), 6 (12-6), and 12 (24-12), which are not the same. This sequence is actually a geometric sequence, as each term is multiplied by 2 to get the next term.
It is neither.
An arithmetic sequence is a series of numbers in which each term is obtained by adding a constant value, called the common difference, to the previous term. In contrast, a geometric sequence is formed by multiplying the previous term by a constant value, known as the common ratio. For example, in the arithmetic sequence 2, 5, 8, 11, the common difference is 3, while in the geometric sequence 3, 6, 12, 24, the common ratio is 2. Thus, the primary difference lies in how each term is generated: through addition for arithmetic and multiplication for geometric sequences.
Give the simple formula for the nth term of the following arithmetic sequence. Your answer will be of the form an + b.12, 16, 20, 24, 28, ...
It is -148.
7
This is not a geometric series since -18/54 is not the same as -36/12