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.
To find the next three terms in the sequence 9, 12, 17, 24, we first identify the differences between consecutive terms: 12 - 9 = 3, 17 - 12 = 5, and 24 - 17 = 7. The differences themselves form an increasing arithmetic sequence: 3, 5, 7. Continuing this pattern, the next differences would be 9, 11, and 13, leading to the subsequent terms being 24 + 9 = 33, 33 + 11 = 44, and 44 + 13 = 57. Therefore, the next three terms are 33, 44, and 57.
In order to determine whether or not this is an arithmetic sequence, there must be at least 3 numbers.
The next is 3.
To find the 18th term of the arithmetic sequence 3, 10, 17, 24..., first, identify the common difference. The difference between consecutive terms is 7 (10 - 3, 17 - 10, 24 - 17). The formula for the nth term of an arithmetic sequence is given by ( a_n = a_1 + (n - 1)d ), where ( a_1 ) is the first term and ( d ) is the common difference. For the 18th term: ( a_{18} = 3 + (18 - 1) \times 7 = 3 + 119 = 122 ).
No, geometric, common ratio 2
It is -148.
It is the start of an arithmetic sequence.
If one may choose the break points, it looks like simple doubling: 3 - 6 - 12 - 24
In order to determine whether or not this is an arithmetic sequence, there must be at least 3 numbers.
No it is not.U(2) - U(1) = 6 - 2 = 4U(3) - U(2) = 18 - 6 = 12Since 4 is different from 12, it is not an arithmetic sequence.
No, it is not.
One of the simplest arithmetic arithmetic sequence is the counting numbers: 1, 2, 3, ... . The person who discovered that is prehistoric and, therefore, unknown.
The next is 3.
Each number is got by adding an amount two larger than the last amount added. 9 (+3) 12 (+5) 17 (+7) 24.Continuing this we get 33, 44 and 57.
It is: -3072
It is: -3072