Question

Monica measures the number of bacteria that are living on her petri dish. Each day, she measures the amount of change in the number of bacteria. These amounts create a geometric sequence. Use the data in the table to determine the sum of the amounts of change in the bacteria after the seventh day. Day Amount of Change in Bacteria 1 2 2 −8 3 32 4 −128 −6553.2 −10.8 6554 11.6

Answer 1

Answer:

  6554

Step-by-step explanation:

The sequence 2, -8, 32, -128 has a first term (a1) of 2 and a common ratio (r) of -8/2 = -4. The sum of n terms is given by ...

  Sn = a1·(r^n -1)/(r -1)

For your sequence, the sum of 7 terms is ...

  S7 = 2·((-4)^7 -1)/(-4-1) = 2(-16384/-5) = 6554

The sum of changes after the 7th day is 6554.