## An initial investment of $3 is worth$108 after 5 years. If the annual growth reflects a geometric sequence, approximately how much will the

Question

An initial investment of $3 is worth$108 after 5 years. If the annual growth reflects a geometric sequence, approximately how much will the investment be worth after 11 years?

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1 week 2021-09-13T15:15:47+00:00 2 Answers 0

The investment be worth $23328 after 11 years. Step-by-step explanation: It is given that the annual growth reflects a geometric sequence. An initial investment of$3 is worth $108 after 5 years. It means the initial value of first term of the gp, a₁ = 3 The 5th term of the gp, a₅ = 108 The nth term of a gp is …. (1) where, a is first term and r is common ratio. The 5th term of the gp is From the given information it is clear that the 5th term of the gp is 108. Substitute a₅ = 108 and a=3. Divide both sides by 3.  Taking fourth root on both the sides. Substitute r=√6, a=3 and n=11 to find the investment worth after 11 years.   Therefore the investment worth$23328 after 11 years.
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