What is the 11th term of the geometric sequence 178, 106.8, 64.08, ...? A

0.39

B

0.65

С

1.08

D

1.79

Step-by-step explanation:

step 1. A geometric sequence is found by multiplying subsequent term by a number r.

step 2. 106.8/178 = 0.6. 64.08/106.8 = 0.6. a = 0.6. note that a geometric series must have the same number when dividing successive terms.

step 3. an = ar^(n - 1) = a(0.6)^(n - 1)

step 4. given a1 = 178. an = 178(0.6)^(n - 1)

step 5. therefore a11 is the 11th term!

step 6. a11 = 178(0.6)^10 = 1.0763 = 1.08.

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