Geometric Sequence find the 23rd term.

In summary, a geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant number, the common ratio. To find the common ratio, you divide any term in the sequence by the previous term. The formula for finding the n-th term of a geometric sequence is T<sub>n</sub> = T<sub>1</sub> * r<sup>n-1</sup>, where T<sub>n</sub> is the n-th term, T<sub>1</sub> is the first term, and r is the common ratio. To find the 23rd term of a geometric sequence, you can use the formula T<sub>23</sub> = T<
  • #1
mathdad
1,283
1
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?
 
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  • #2
yes
 
  • #3
a_23 = 25 * 1.8(23-1)

a_23 = 25 * (1.8)^(22)

a_23 = 10326071.3

Correct?
 
  • #4
To one decimal place, yes. Do you have a reason for choosing to write the answer to one decimal place?
 

FAQ: Geometric Sequence find the 23rd term.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant number, called the common ratio.

How do you find the common ratio of a geometric sequence?

To find the common ratio of a geometric sequence, you divide any term in the sequence by the previous term.

What is the formula for finding the n-th term of a geometric sequence?

The formula for finding the n-th term of a geometric sequence is Tn = T1 * rn-1, where Tn is the n-th term, T1 is the first term, and r is the common ratio.

How do you find the 23rd term of a geometric sequence?

To find the 23rd term of a geometric sequence, you can use the formula T23 = T1 * r22, where T1 is the first term and r is the common ratio.

Can you provide an example of finding the 23rd term of a geometric sequence?

Yes, for example, if you have a geometric sequence with a first term of 2 and a common ratio of 3, the 23rd term would be T23 = 2 * 322 = 2 * 1,048,576 = 2,097,152.

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