Emmy is picking berries in the berry patch. She picks 187 berries from the first bush, 169 berries from the second bush, 151 berries from the third bush, and 133 berries from the fourth bush. What kind of sequence is this?...

Question

A) arithmetic
B) geometric
C) both
D) neither

Answer 1

To determine the type of sequence represented by the number of berries Emmy picks from each bush, we can examine the differences between the consecutive terms to see if it's an arithmetic sequence, or examine the ratios of consecutive terms to see if it's a geometric sequence.

1. Arithmetic Sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

   • From the first bush to the second bush: \( 169 - 187 = -18 \)
   • From the second bush to the third bush: \( 151 - 169 = -18 \)
   • From the third bush to the fourth bush: \( 133 - 151 = -18 \)

   Since the differences are all the same (-18), this is an arithmetic sequence.

2. Geometric Sequence: In a geometric sequence, the ratio of consecutive terms is constant.

   • From the first bush to the second bush: \( \frac{169}{187} \approx 0.9037 \)
   • From the second bush to the third bush: \( \frac{151}{169} \approx 0.8917 \)
   • From the third bush to the fourth bush: \( \frac{133}{151} \approx 0.8808 \)

   The ratios are not the same, so it's not a geometric sequence.

Since the sequence is arithmetic and not geometric, the answer is A) arithmetic.