find the sum of the arithmetic series 13+11+9+...+(-25)
clearly,
a = 13
d = -2
-25 = 13+19(-2), so -25 is A20
S20 = 20/2(13-25) = -120
13+12+11+...20terms
To find the sum of an arithmetic series, you can use the formula:
Sum = (n / 2)(first term + last term)
In this case, the first term is 13, and the last term is -25.
To find the number of terms, you need to find the difference between the first and last terms and divide it by the common difference:
Difference = last term - first term = -25 - 13 = -38
Common difference = -2 (since each term is decreasing by 2)
Now, substitute the values into the formula:
Sum = (n / 2)(first term + last term)
= (n / 2)(13 + (-25))
= (n / 2)(-12)
= -6n
To find the number of terms, you can use the formula:
n = (last term - first term) / Common difference + 1
n = (-25 - 13) / (-2) + 1
= (-38) / (-2) + 1
= 19 + 1
= 20
Finally, substitute the value of n into the sum formula:
Sum = -6n
= -6(20)
= -120
The sum of the arithmetic series 13 + 11 + 9 + ... + (-25) is -120.