find g(1)+g(2)+g(3)+...+g(50) given that g(x)=13-5x
this is simply an arithmetic series where
a = 8
d = -5
n = 50
sum(n) = (n/2)[2a + (n-1)d)]
sum(50) = (50/2)[16 + 49(-5)]
= 25[-229]
= -5725
In order to find the sum of g(1) + g(2) + g(3) + ... + g(50), we need to find the value of g(x) for each value of x and add them all together.
The given function is g(x) = 13 - 5x.
To find g(1), substitute x = 1 into the function:
g(1) = 13 - 5(1) = 13 - 5 = 8.
To find g(2), substitute x = 2 into the function:
g(2) = 13 - 5(2) = 13 - 10 = 3.
Following the same process, we can find the values of g(x) for each x from 1 to 50 and then add them together.
g(3) = 13 - 5(3) = 13 - 15 = -2.
g(4) = 13 - 5(4) = 13 - 20 = -7.
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g(50) = 13 - 5(50) = 13 - 250 = -237.
Now, add up all the values of g(x) from g(1) to g(50).
g(1) + g(2) + g(3) + ... + g(50) = 8 + 3 + (-2) + (-7) + ... + (-237).
You can also find the sum using the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the nth term.
In this case, a1 = g(1) = 8, an = g(50) = -237, and there are 50 terms (1 to 50). Plugging these values into the formula, we get:
Sn = (50/2)(8 + (-237)) = (25)(-229) = -5725.
Therefore, g(1) + g(2) + g(3) + ... + g(50) = -5725.