Write and explicit formula for the following sequence. Then generate the first five terms.
A1= 625
R=0.2
A1 = 625
An = A1 * r^(n-1)
Now plug in your numbers and crank 'em out.
what the fric
To find the explicit formula for the given sequence, we need to identify the pattern in the terms.
The given sequence is A1 = 625, and the common ratio (R) is 0.2.
The terms of the geometric sequence can be obtained using the formula:
An = A1 * R^(n-1)
Substituting the given values:
An = 625 * 0.2^(n-1)
To generate the first five terms, we substitute n with the values 1, 2, 3, 4, and 5:
A1 = 625 * 0.2^(1-1) = 625 * 0.2^0 = 625 * 1 = 625
A2 = 625 * 0.2^(2-1) = 625 * 0.2^1 = 625 * 0.2 = 125
A3 = 625 * 0.2^(3-1) = 625 * 0.2^2 = 625 * 0.04 = 25
A4 = 625 * 0.2^(4-1) = 625 * 0.2^3 = 625 * 0.008 = 5
A5 = 625 * 0.2^(5-1) = 625 * 0.2^4 = 625 * 0.0016 = 1
Therefore, the first five terms of the sequence are: 625, 125, 25, 5, 1.
To find the explicit formula for the given sequence, we need to determine the pattern that describes how each term is related to the previous term.
The given sequence has a common ratio of 0.2, which means each term can be obtained by multiplying the previous term by 0.2. Thus, the explicit formula for this sequence can be determined as:
An = A1 * r^(n-1)
Where:
- An represents the nth term of the sequence.
- A1 represents the first term of the sequence.
- r represents the common ratio of the sequence.
- n represents the position of the term in the sequence.
Let's generate the first five terms of this sequence using the formula:
A1 = 625 (Given)
A2 = A1 * r^(2-1) = 625 * 0.2^1 = 125
A3 = A1 * r^(3-1) = 625 * 0.2^2 = 25
A4 = A1 * r^(4-1) = 625 * 0.2^3 = 5
A5 = A1 * r^(5-1) = 625 * 0.2^4 = 1
Therefore, the first five terms of the sequence are 625, 125, 25, 5, 1.