Question

HELP PLEASE!!!

I still can't figure this out. How do you solve these type of equations? The question goes like this...

Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum.

50+55+60+...; n=7

Please I am begging, can someone show me how to solve this. I seriously am desperate right now.

Answer 1

So if you're going from n = 1 to n = 7 then how do we figure this out? Well, essentially you are just make a function that when you evaluate it at 1 you get 50. At 2 you get 55. At 3 you get 60.

f(1)=50
f(2)=55
f(3)=60
...

So now we can sort of see that each time we count up by 1 we move up by 5. So there's gotta be a term that looks like:

g(n)=5n

But that's not quite right. If we plug in numbers we get:

g(1)=5
g(2)=10
g(3)=15
...

So what are we missing? Just add 45 to each one to get what we need!

f(x)=5n+45

So now we have exactly what we wanted. You just sorta have to think about them and figure them out. Don't be afraid to play around and take guesses on these and try to find patterns and just try to get closer and closer until you figure it out kinda like I did when I made a guess that g(n) was 5n, even though it was off we were still able to use it to see how close we were to our next guess.

Now just put on the summation sign from n =1 to n = 7.