Geometric Sequences Practice

Question

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Question
Bacteria quadruples on a daily basis. The population starts with 50 bacteria. Using the general exponential equation an=a1⋅rn−1
, what value would represent a1
?(1 point)
The value of a1
is
.
Remaining Attempts : 3

Answer 1

In the general formula for a geometric (exponential) sequence given by \( a_n = a_1 \cdot r^{(n-1)} \):

• \( a_1 \) represents the first term of the sequence,
• \( r \) is the common ratio, and
• \( n \) is the term number.

In the context of the bacteria population:

• The initial population of bacteria (when \( n = 1 \)) is given as 50. Therefore, \( a_1 = 50 \).
• The population quadruples daily, which means the common ratio \( r = 4 \).

Thus, the value of \( a_1 \) is 50.