I don't understand why this is the answer (sigma notation) MEDALS

Question

anonymous · Answer

attachment

anonymous · Answer

first to get it right gets to mate with me!

anonymous · Answer

That's embarrassing. Ma'am, we're here to ask or answer questions. Not sell ourselves online. 

Please get your act together.

rock_mit182 · Answer

the only thing i know is the girl in the pictuare is hot! LOL

anonymous · Answer

;)

anonymous · Answer

Studied this problem a little, found something interesting. 
Basically this notation is saying: "Add up the first 'n' terms in the sequence (9k+5), while k=1." The confusing bit is that I don't know what 'n' terms represents. I plugged in pi instead of 'n' to see what the result would be. I got 74.74. Then I took that answer, went back to the answer of the problem you presented, and substituted pi in for n. 

(1/2)pi(9pi + 19) turned out to be 74.30! That's just shy of 74.74...Would N = Pi? This is a very interesting problem. I'm going to look into it a little more, see what I can find.

anonymous · Answer

Also, I hope I didn't offend you in any way. That's not my intent. 

But ma'am, we must take care. There are children on this site too; we must set an example.

anonymous · Answer

hey thanks for the help dude. no offense taken, im a dude

anonymous · Answer

pi? lol
the answer is right

anonymous · Answer

i know the answer is right, i just want an explanation for it

anonymous · Answer

please

anonymous · Answer

A dude, huh? It's always good to be enlightened. Hey, I'm working through this thing right now. I'll get back to you when I see the light! :D

anonymous · Answer

ooh i see sorry, i thought you wanted to see why it was wrong
there are two ways to solve this

anonymous · Answer

ok whats the fastest

anonymous · Answer

this way
the first term is what you get when you replace $k$ by $1$ namely $9\times 1+5=14$
the last term is what you get when you replace $k$ by $n$ i.e. $9n+5$
add them together and get $9n+5+14=9n+19$ multiply by $n$  then divide by $2$ and get 
$$\frac{1}{2}n(9n+19)$$

anonymous · Answer

one half times the first term plus the last term times the number of terms is the "formula"

anonymous · Answer

nice, you're a winner. thanks pal

anonymous · Answer

yw

anonymous · Answer

That's beautiful. Thanks S73! You made my day.