What is 17+18+19+...+42+43
The sum of the numbers from 17 to 43 can be found using the formula for the sum of an arithmetic series:
S = (n/2)(2a + (n-1)d)
where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, a = 17, d = 1, and we need to find the value of n.
To find the number of terms, we can use the formula for the nth term of an arithmetic series:
an = a + (n-1)d
Since 43 is the last term, we have:
43 = 17 + (n-1)(1)
43 - 17 = n - 1
26 = n - 1
n = 27
Now we can find the sum using the formula:
S = (n/2)(2a + (n-1)d)
S = (27/2)(2(17) + (27-1)(1))
S = (27/2)(34 + 26)
S = (27/2)(60)
S = 27(30)
S = 810
Therefore, the sum of the numbers from 17 to 43 is 810.
What is 75+72+69+66+...+21+18+15?
To find the sum of the given sequence, we can use the formula for the sum of an arithmetic series:
S = (n/2)(2a + (n-1)d)
where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, a = 75, d = -3, and we need to find the value of n.
To find the number of terms, we can use the formula for the nth term of an arithmetic series:
an = a + (n-1)d
Since 15 is the last term, we have:
15 = 75 + (n-1)(-3)
15 - 75 = -3n + 3
-60 = -3n + 3
-63 = -3n
n = 21
Now we can find the sum using the formula:
S = (n/2)(2a + (n-1)d)
S = (21/2)(2(75) + (21-1)(-3))
S = (21/2)(150 + 20(-3))
S = (21/2)(150 - 60)
S = (21/2)(90)
S = 21(45)
S = 945
Therefore, the sum of the numbers from 75 to 15 is 945.