MHB Geometric Sequence find the 23rd term.

AI Thread Summary
The function for the geometric sequence is defined as a_n = a_1•r^(n-1), where a_1 is the initial value of 25 and r is the common ratio of 1.8. To find the 23rd term, the calculation is a_23 = 25•(1.8)^(22), resulting in a_23 = 10326071.3. The answer is confirmed to be correct when rounded to one decimal place. The discussion also touches on the rationale for presenting the answer to one decimal place.
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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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