Find the rule for 9,16.8, 24.6, 32.4
16.8 - 9 = 7.8
i left out the part that you need to put it in nth term
a(n)=a(n-1)+7.8
OR
a(n)=a1+(n-1)*d
a(n)=9+(n-1)*7.8
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arithmetic progression
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To find the rule for the given sequence of numbers: 9, 16.8, 24.6, 32.4, we need to determine the pattern or relationship between the terms.
Looking at the sequence, we can observe that each number is obtained by multiplying the previous number by a constant factor.
Let's analyze the differences between the terms:
16.8 - 9 = 7.8
24.6 - 16.8 = 7.8
32.4 - 24.6 = 7.8
We notice that the differences between consecutive terms are the same (7.8). This indicates that the sequence follows a linear pattern.
Now, let's find the common factor that is multiplied to obtain each term. We can divide any term by the previous term:
16.8 / 9 ≈ 1.8667
24.6 / 16.8 ≈ 1.4643
32.4 / 24.6 ≈ 1.3171
We can see that the quotients are relatively close but not exactly the same. However, there is a clear downward trend in the values, indicating that the common factor might be decreasing.
Let's calculate the differences between consecutive quotients:
1.4643 - 1.8667 ≈ -0.4024
1.3171 - 1.4643 ≈ -0.1472
The differences between the quotients are not consistent. Therefore, we conclude that the sequence does not follow a geometric progression.
Since we know it follows a linear pattern, let's write the general equation for a linear sequence:
n = a + (d x (x - 1))
Where:
n = the value of the term
a = the first term of the sequence
d = the common difference between terms
x = the position of the term in the sequence
Now, let's substitute the first term, seventh term, and the position (x) to find the value of the seventh term (n):
a = 9
d = 7.8
x = 7
n = 9 + (7.8 x (7 - 1))
n = 9 + (7.8 x 6)
n = 9 + 46.8
n = 55.8
Therefore, applying the rule found, the seventh term of the sequence is 55.8.
In conclusion, the rule for the given sequence is a linear progression with a common difference of 7.8. Using the equation n = a + (d x (x - 1)), you can find the value of any term by substituting the values of the first term, common difference, and the position in the sequence.