Question

"Which of the following sequences can be described as an arithmetic sequence? (Select all that apply.)

a) {9, 10, 12, 15, 19, …}
b) {-9, -3, 3, 9, 16, …}
c) {7, 1, -5, -11, -17, …}
d) {7, 15, 23, 31, 38, …}
e) {6, 4, 2, 0, -2, …}
f) {-10, -30, -90, -270, -810, …}

Answer 1

Among the given options, c) {7, 1, -5, -11, -17, …} and e) {6, 4, 2, 0, -2, …} are arithmetic sequences because they have a consistent common difference between consecutive terms.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers with a common difference between consecutive terms. To determine if a sequence is arithmetic, we calculate the difference between successive terms and see if this difference is consistent.

• a) {9, 10, 12, 15, 19, …} - This is not an arithmetic sequence because the differences between terms are 1, 2, 3, 4, which are not consistent.
• b) {-9, -3, 3, 9, 16, …} - This is not an arithmetic sequence as the differences are 6, 6, 6, 7, which are not all the same.
• c) {7, 1, -5, -11, -17, …} - This is an arithmetic sequence. The common difference is -6.
• d) {7, 15, 23, 31, 38, …} - This is not an arithmetic sequence because the differences are 8, 8, 8, 7, which are not all the same.
• e) {6, 4, 2, 0, -2, …} - This is an arithmetic sequence with a common difference of -2.
• f) {-10, -30, -90, -270, -810, …} - This is not an arithmetic sequence; instead, it's a geometric sequence because each term is multiplied by 3 to get to the next term.

Thus, the sequences in options c) and e) can be described as arithmetic sequences.