Geometric Sequence find the 23rd term.

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Discussion Overview

The discussion revolves around finding the 23rd term of a geometric sequence with an initial value of 25 and a common ratio of 1.8. Participants explore the formulation of the sequence and the calculation of the specific term.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the function for the geometric sequence as a_n = a_1•r^(n-1) and calculates a_23 = 25•(1.8)^(23 - 1).
  • Another participant confirms the calculation is correct.
  • A different participant reformulates the expression for a_23 as 25 * (1.8)^(22) and computes the value as approximately 10326071.3.
  • One participant agrees with the computed value to one decimal place and inquires about the reasoning behind that level of precision.

Areas of Agreement / Disagreement

There is agreement on the correctness of the calculations, but the discussion includes a question regarding the choice of precision in the final answer.

Contextual Notes

Participants have not explicitly discussed the implications of rounding or the significance of the precision chosen for the answer.

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A geometric sequence has an initial value of 25 and a common ratio of 1.8. Write a function to represent this sequence . Find the 23rd term.

My Effort:

The needed function is

a_n = a_1•r^(n-1), n is the 23rd term, r is the common ratio and a_1 is the initial value.

a_23 = 25•(1.8)^(23 - 1)

Is this correct?
 
Mathematics news on Phys.org
yes
 
a_23 = 25 * 1.8(23-1)

a_23 = 25 * (1.8)^(22)

a_23 = 10326071.3

Correct?
 
To one decimal place, yes. Do you have a reason for choosing to write the answer to one decimal place?
 

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