The sum of the first 21 term of the progression _18,_15,_12,___is
252
hehehawhaw
To find the sum of the first 21 terms of the arithmetic progression _18, _15, _12, ___, we need to determine the common difference first.
From the given progression, we can observe that each term is decreasing by 3.
Now, we can calculate the sum using the formula for the sum of an arithmetic series:
S = (n/2) * (a₁ + aₙ)
Where:
S = Sum of the series
n = Number of terms
a₁ = First term
aₙ = Last term
In this case:
n = 21 (since we want to find the sum of the first 21 terms)
a₁ = 18 (the first term)
aₙ = ?
To find aₙ, we can use the formula for the nth term of an arithmetic progression:
aₙ = a₁ + (n-1) * d
Where:
d = Common difference
In this case:
d = -3 (since each term is decreasing by 3)
Substituting the values into the formula, we can find aₙ:
aₙ = 18 + (21-1) * -3
= 18 + 20 * -3
= 18 - 60
= -42
Now that we have aₙ, we can calculate the sum of the series:
S = (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.
To find the sum of the first 21 terms of the given arithmetic progression (_18, _15, _12, ...), we need to determine the common difference.
In an arithmetic progression, each term is obtained by adding a constant difference to the previous term. To find this difference, we subtract the second term from the first term:
_15 - _18 = -3
So, the common difference is -3.
Now, we can find the 21st term of the progression by adding the common difference to the first term:
_18 + (-3 * (21 - 1)) = _18 + (-3 * 20) = _18 - 60 = _(-42)
The 21st term is _(-42).
To calculate the sum of the first 21 terms, we can use the formula for the sum of an arithmetic progression:
Sum = (n/2) * (first term + last term)
Substituting the values we have:
Sum = (21/2) * (_18 + _(-42))
Sum = 10.5 * (_18 - 42)
Sum = 10.5 * _(-24)
Sum = _(-252)
Therefore, the sum of the first 21 terms of the given arithmetic progression is _(-252).