Question

While sorting some beads, Trudy put 77 beads in the first jar, 64 beads in the second jar, 51 beads in the third jar, and 38 beads in the fourth jar. What kind of sequence is this?

Answer 1

To determine the type of sequence formed by the number of beads in each jar, we can examine the differences between the consecutive numbers.

We have the following number of beads in the jars:
- First jar: 77
- Second jar: 64
- Third jar: 51
- Fourth jar: 38

Now, let's calculate the differences between consecutive jars:

1. Difference between the first and second jar: \( 77 - 64 = 13 \)
2. Difference between the second and third jar: \( 64 - 51 = 13 \)
3. Difference between the third and fourth jar: \( 51 - 38 = 13 \)

Since the differences between each consecutive pair are constant (all equal to 13), this indicates that the sequence is an **arithmetic sequence**.

In summary, Trudy's beads in the jars create an arithmetic sequence with a common difference of -13 between each consecutive jar.