The sum of the 21 terms of the progression:-18,-15,-12
The given arithmetic progression starts with -18 and has a common difference of +3.
To find the sum of the 21 terms, we can use the formula for the sum of an arithmetic series:
S = (n/2)(2a + (n-1)d),
where:
S = sum of the series
n = number of terms
a = first term
d = common difference
In this case, n = 21, a = -18, and d = +3. Plugging these values into the formula, we get:
S = (21/2)(2(-18) + (21-1)(3))
S = (21/2)(-36 + 20(3))
S = (21/2)(-36 + 60)
S = (21/2)(24)
S = 21(12) = 252.
Therefore, the sum of the 21 terms in the given arithmetic progression is 252.
To find the sum of the terms of an arithmetic progression, we need to know the first term, the common difference, and the number of terms in the progression.
Given the first three terms of the arithmetic progression: -18, -15, -12, we can determine the common difference by subtracting any two successive terms.
Common Difference = -15 - (-18) = 3
Now that we know the common difference, we can find the 21st term of the progression by using the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
21st term = -18 + (21 - 1) * 3 = -18 + 20 * 3 = -18 + 60 = 42
So, the 21st term of the arithmetic progression is 42.
Now let's calculate the sum of the first 21 terms using the formula for the sum of an arithmetic sequence:
Sum = (number of terms / 2) * (first term + last term)
Sum = (21 / 2) * (-18 + 42) = 10.5 * 24 = 252
Therefore, the sum of the 21 terms in the arithmetic progression -18, -15, -12 is 252.
To find the sum of the 21 terms of the given arithmetic progression, we need to first find the common difference (d) between the terms.
In an arithmetic progression, the common difference (d) is the constant value by which each term increases or decreases. To find it, we can subtract any two consecutive terms.
In this case, let's subtract the second term (-15) from the first term (-18):
d = -15 - (-18) = -15 + 18 = 3
Therefore, the common difference (d) is 3.
Next, we can use the formula to find the sum of an arithmetic progression:
Sn = (n/2) * (2a + (n - 1) * d)
Where:
Sn = sum of the first n terms
a = first term of the progression
d = common difference between the terms
n = number of terms
In this case, we are given the first term (a = -18), common difference (d = 3), and number of terms (n = 21). Plugging these values into the formula:
S21 = (21/2) * (2 * -18 + (21 - 1) * 3)
Simplifying further:
S21 = (21/2) * (-36 + 20 * 3)
S21 = 21/2 * (-36 + 60)
S21 = 21/2 * 24
S21 = 21 * 12
S21 = 252
Therefore, the sum of the 21 terms of the given arithmetic progression is 252.