+0

# help:(:)

+7
62
3
+203

What is the value of the arithmetic series 28+30+32+...+86?

Jan 4, 2020

#1
+31
+2

You can evaluate it as the difference of two sums (relating problems to similar problems).

One sum is 0+2+4+6+8+...+86.

Jan 4, 2020
#2
+1035
0

Solution: 1,710

Divide the series by two; we can multiply by 2 later.

14+15+16+...+42+43.

The formula of finding the sum of the first $$n$$ positive integers is $$\frac{n \times (n+1)}{2}$$.

We can first find the sum until 43, then subtract the sum until 13 to get the value of 14+15+16+...+42+43.

First plugging in 43, we get $$\frac{43 \times (43+1)}{2} = 946$$.

Then plugging in 13, we get $$\frac{13 \times (13+1)}{2} = 91$$.

$$946-91=855$$.

We still need to multiply by 2 to get our final answer.

$$855 \times 2 = 1710$$.

You are very welcome!

:P

Jan 5, 2020
#3
+203
+7

thanks!

Jan 5, 2020