The sum of the first 21 terms of the progression -10,-8,-6
The given arithmetic progression can be written as -10, -8, -6,...
We can see that the common difference is 2 (add 2 to each term to get the next term).
The formula to find the sum of the first n terms of an arithmetic progression is:
S = (n/2) * (first term + last term)
In this case, the first term is -10 and the last term can be found by adding 2 to the first term 20 times (since there are 21 terms).
Last term = -10 + (20 * 2) = -10 + 40 = 30
Substituting these values into the formula, we get:
S = (21/2) * (-10 + 30) = (21/2) * 20 = 21 * 10 = 210
Therefore, the sum of the first 21 terms of the given arithmetic progression is 210.
To find the sum of the first 21 terms of the arithmetic progression -10, -8, -6, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d),
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
In this case, a = -10, d = 2 (because the terms are increasing by 2), and n = 21.
Substituting these values into the formula, we get:
S21 = (21/2)(2(-10) + (21-1)(2))
= (21/2)(-20 + 20)
= (21/2)(0)
= 0.
Therefore, the sum of the first 21 terms of the progression -10, -8, -6 is 0.
To find the sum of the first 21 terms of the given arithmetic progression, we need to use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = (n/2) * (a + l),
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
First, let's find the last term of the series. We know that the common difference between consecutive terms is 2, so we can find the last term using the formula:
l = a + (n - 1) * d,
where d is the common difference.
In this case, the first term a is -10, the common difference d is 2, and the number of terms n is 21. Plugging in these values, we can find the last term:
l = -10 + (21 - 1) * 2 = -10 + 20 * 2 = -10 + 40 = 30.
Now that we know the first term a (-10), the last term l (30), and the number of terms n (21), we can calculate the sum S:
S = (n/2) * (a + l) = (21/2) * (-10 + 30) = (21/2) * 20 = 210.
Therefore, the sum of the first 21 terms of the progression -10, -8, -6, ... is 210.