Select ALL of the following that are examples of an arithmetic sequence.
Responses
1, 11, 21, 25, 31, 38
1, 11, 21, 25, 31, 38
You add $2 to a piggy bank and add triple the money you added the previous day for one month.
You add $2 to a piggy bank and add triple the money you added the previous day for one month.
20, 14, 8, 2, −4, −10
20, 14, 8, 2, −4, −10
3, 9, 27, 81, 243
3, 9, 27, 81, 243
You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
4,000 feet
3,000 feet
2,000 feet
1,000 feet
0 feet
-1,000 feet
20, 14, 8, 2, −4, −10
constant difference of -6
1,000 feet per day. (constant difference of -1000)
BY THE WAY 3, 9, 27, 81, 243 is a GEOMETRIC sequence with ratio of 3
Apologies for the mistake. You are correct. The sequence 3, 9, 27, 81, 243 is a geometric sequence, not an arithmetic sequence. Thank you for pointing that out.
To determine if a sequence is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.
Let's examine each option:
1, 11, 21, 25, 31, 38:
The difference between consecutive terms is not constant. For example, the difference between the first two terms is 11 - 1 = 10, while the difference between the second and third terms is 21 - 11 = 10. However, the difference between the fourth and fifth terms is 31 - 25 = 6, which breaks the pattern. Therefore, this sequence is not an arithmetic sequence.
You add $2 to a piggy bank and add triple the money you added the previous day for one month:
This is not a sequence but rather an instruction or a process. It describes how to add money to a piggy bank, but it doesn't provide a definite list of numbers. Therefore, this does not represent an arithmetic sequence.
20, 14, 8, 2, -4, -10:
The difference between consecutive terms in this sequence is -6. For example, 14 - 20 = -6, and 8 - 14 = -6. This pattern continues, so the sequence is an arithmetic sequence.
3, 9, 27, 81, 243:
The difference between consecutive terms is 6. For example, 9 - 3 = 6, and 27 - 9 = 18. This difference remains constant, so the sequence is an arithmetic sequence.
You start at an elevation of 12,000 feet and climb down 1,000 feet per day:
Similar to the second option, this is not a sequence but rather describes a process. It provides information on how elevation changes, but it does not give a list of numbers.
In summary, the arithmetic sequences among the given options are:
20, 14, 8, 2, -4, -10
3, 9, 27, 81, 243