Select the sequences that are geometric. 8 18,36,54,72,ldots 4.1,8.2,16.4,32.8,ldots -7,14,-28,56,ldots 980,784,627.2,501.76,ldots 5,2,-1,-4,ldots COMPLETE Which statements describe characteristics of a geometric sequence? Check all that apply. There is a common difference between terms Each term is multiplied by the same number to arrive at the next term. The sequence increases or decreases in a linear pattern There is a common ratio between terms. DONE

To determine which sequences are geometric, we need to check if there is a common ratio between each term. A geometric sequence is defined by the property that each term is obtained by multiplying the previous term by a constant factor.<br /><br />Let's analyze each sequence:<br /><br />1. $18, 36, 54, 72, \ldots$<br /> - The ratio between consecutive terms is not constant (36/18 = 2, 54/36 = 1.5, 72/54 ≈ 1.33). This sequence is not geometric.<br /><br />2. $4.1, 8.2, 16.4, 32.8, \ldots$<br /> - The ratio between consecutive terms is constant (8.2/4.1 = 2, 16.4/8.2 = 2, 32.8/16.4 = 2). This sequence is geometric.<br /><br />3. $-7, 14, -28, 56, \ldots$<br /> - The ratio between consecutive terms is constant (-14/-7 = -2, -28/14 = -2, 56/-28 = -2). This sequence is geometric.<br /><br />4. $980, 784, 627.2, 501.76, \ldots$<br /> - The ratio between consecutive terms is constant (784/980 = 0.8, 627.2/784 = 0.8, 501.76/627.2 ≈ 0.8). This sequence is geometric.<br /><br />5. $5, 2, -1, -4, \ldots$<br /> - The ratio between consecutive terms is not constant (2/5 = 0.4, -1/2 = -0.5, -4/-1 = 4). This sequence is not geometric.<br /><br />Based on the analysis, the geometric sequences are:<br />- $4.1, 8.2, 16.4, 32.8, \ldots$<br />- $-7, 14, -28, 56, \ldots$<br />- $980, 784, 627.2, 501.76, \ldots$<br /><br />Characteristics of a geometric sequence:<br />- Each term is multiplied by the same number to arrive at the next term.<br />- There is a common ratio between terms.<br /><br />Therefore, the statements that describe characteristics of a geometric sequence are:<br />- Each term is multiplied by the same number to arrive at the next term.<br />- There is a common ratio between terms.