Giving the following progression. 4,6,8,10 and then find a)10th,b)11th,c)26th
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well, just plug in the numbers in your formula:
An = 2+2n
To find the terms of a progression, we need to identify the pattern or rule that governs the series. In this case, we can see that the progression is an arithmetic series because the terms increase by a constant difference.
The given progression is:
4, 6, 8, 10
We can observe that each term increases by 2. Therefore, the common difference (d) is 2.
To find the nth term (Tn) of an arithmetic series, we can use the formula:
Tn = a + (n - 1) * d
Where:
Tn is the nth term
a is the first term
n is the position of the term
d is the common difference
Let's calculate the required terms.
a) To find the 10th term:
n = 10
a = 4
d = 2
T10 = 4 + (10 - 1) * 2
T10 = 4 + 9 * 2
T10 = 4 + 18
T10 = 22
Therefore, the 10th term is 22.
b) To find the 11th term:
n = 11
a = 4
d = 2
T11 = 4 + (11 - 1) * 2
T11 = 4 + 10 * 2
T11 = 4 + 20
T11 = 24
Therefore, the 11th term is 24.
c) To find the 26th term:
n = 26
a = 4
d = 2
T26 = 4 + (26 - 1) * 2
T26 = 4 + 25 * 2
T26 = 4 + 50
T26 = 54
Therefore, the 26th term is 54.
By applying the formula for an arithmetic series, we were able to find the 10th, 11th, and 26th terms of the given progression.