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.
mathdad
Messages
1,280
Reaction score
0
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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Replies
3
Views
2K
Replies
5
Views
2K
Replies
1
Views
2K
Replies
2
Views
3K
Replies
1
Views
2K
Replies
22
Views
5K
Replies
3
Views
3K
Replies
2
Views
3K
Back
Top