The sum of the first 21 terms of the progression,-18-15-12 is
The given progression is an arithmetic progression with a common difference of 3. The formula to find the sum of the first n terms of an arithmetic progression is:
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, the first term (a) is -18 and the common difference (d) is 3. We want to find the sum of the first 21 terms (n = 21). Plugging these values into the formula, we get:
Sn = (21/2)(2(-18) + (21-1)(3))
= (21/2)(-36 + 20(3))
= (21/2)(-36 + 60)
= (21/2)(24)
= 21(12)
= 252
Therefore, the sum of the first 21 terms of the progression -18, -15, -12 is 252.
The given progression is -18, -15, -12. This is an arithmetic progression with a common difference of 3 (each term increases by 3).
To find the sum of the first 21 terms of this arithmetic progression, 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 (since we're summing the first 21 terms)
a = -18 (the first term)
d = 3 (the common difference)
Plugging these values into the formula, we get:
S = (21/2)(2(-18) + (21-1)3)
Simplifying further:
S = (21/2)(-36 + 20(3))
S = (21/2)(-36 + 60)
S = (21/2)(24)
S = 21 * 12
S = 252
Therefore, the sum of the first 21 terms of the progression -18, -15, -12 is 252.
To find the sum of the terms in a arithmetic progression, you can use the formula for the sum of an arithmetic series. The formula is:
Sn = n/2 * (a + L)
Where Sn is the sum of the terms, n is the number of terms, a is the first term, and L is the last term.
In this case, the progression is -18, -15, -12, and the first term is -18. We need to find the sum of the first 21 terms.
To find the last term, we can use the formula for the nth term of an arithmetic progression:
an = a + (n-1) * d
Where an is the nth term, a is the first term, n is the term number, and d is the common difference.
In this case, the common difference is 3 (since we add 3 to each term to get the next term). So the 21st term would be:
a21 = -18 + (21-1) * 3
= -18 + 20 * 3
= -18 + 60
= 42
Now we can calculate the sum of the first 21 terms using the sum formula:
Sn = n/2 * (a + L)
= 21/2 * (-18 + 42)
= 21/2 * 24
= 21 * 12
= 252
Therefore, the sum of the first 21 terms of the progression -18, -15, -12 is 252.