The sum of the first 21 term of the progression -18 -15 -12
The sum of the first 21 terms of the progression is -378.
The bot is wrong!!!!
a = -18, d = 3, n=21
sum(21) = (21/2)(-36 + 20(3))
= (21/2)(24)
= 21(12) = 252
To find the sum of the first 21 terms of the arithmetic progression -18, -15, -12, we will use the formula for the summation of an arithmetic series, which is given by:
Sn = (n/2) * (2a + (n-1)d)
where:
Sn = sum of the series
n = number of terms
a = first term
d = common difference
In this case, the first term (a) is -18, the common difference (d) is 3 (since 3 is added to each term to get the next term), and the number of terms (n) is 21.
Now, 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.
To find the sum of the first 21 terms of the arithmetic progression -18, -15, -12, we can use the formula for the sum of an arithmetic series.
The general formula for the sum of an arithmetic series is Sn = (n/2) * (a1 + an), where Sn represents the sum of the series, n is the number of terms, a1 is the first term, and an is the nth term.
In this case, a1 = -18 (the first term) and n = 21 (the number of terms) because we want to find the sum of the first 21 terms.
To find the value of the 21st term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where d is the common difference.
In this case, d = -15 - (-18) = -15 + 18 = 3.
Substituting the values into the formula, we have:
an = -18 + (21 - 1) * 3 = -18 + 20 * 3 = -18 + 60 = 42.
Now, we can substitute the values into the sum formula:
Sn = (21/2) * (-18 + 42) = 21 * 24 = 504.
Therefore, the sum of the first 21 terms of the arithmetic progression -18, -15, -12 is 504.