OpenStudy (lilymq):

What is the sum of a 23-term arithmetic sequence where the first term is 9 and the last term is 119?

2 years ago
OpenStudy (lilymq):

Is it 1472? That's what I got

2 years ago
OpenStudy (jhannybean):

First define what an arithmetic sum is.

2 years ago
OpenStudy (solomonzelman):

i think you are a little off

2 years ago
OpenStudy (lilymq):

So it's wrong?

2 years ago
OpenStudy (solomonzelman):

\(\large\color{black}{ \displaystyle a_9=9 }\) \(\large\color{black}{ \displaystyle a_{23}=119 }\) \(\large\color{black}{ \displaystyle {\rm S}_{23-9}=\frac{\left(a_9+a_{23}\right)}{2} \times(23-9) }\) \(\large\color{black}{ \displaystyle {\rm S}_{23-9}=\frac{\left(9+199\right)}{2} \times(23-9) }\)

2 years ago
OpenStudy (solomonzelman):

where 23-9 is the number of terms, and the first fraction is the average term

2 years ago
OpenStudy (lilymq):

is it 1456?

2 years ago
OpenStudy (jhannybean):

That is, \[\large S_n=\frac{n(a_1+a_n)}{2}\]To find \(a_n\) we need to use an arithmetic sequence, \(a_n = a_1 +(n-1)d\)

2 years ago
OpenStudy (lilymq):

okay

2 years ago
OpenStudy (solomonzelman):

we know the 23rd term, Jhanny....

2 years ago
OpenStudy (jhannybean):

Yeah I just reread it haha

2 years ago
OpenStudy (solomonzelman):

i think all you need is last+first term \(a_{23}\) and \(a_9\) in this case....

2 years ago
OpenStudy (solomonzelman):

alright....

2 years ago
OpenStudy (solomonzelman):

1456 is right....

2 years ago
OpenStudy (solomonzelman):

1456 apples, jk

2 years ago
OpenStudy (jhannybean):

but whats with the multiplication?

2 years ago
OpenStudy (lilymq):

then what?

2 years ago
OpenStudy (solomonzelman):

multiplication ?

2 years ago
OpenStudy (solomonzelman):

(9+199)÷2 => the average term 23-9 = number of terms (9+199)÷2 • (23-9) = the sum of all terms together

2 years ago
OpenStudy (jhannybean):

\[\large S_{23} = \frac{23(9+119)}{2}\]

2 years ago
OpenStudy (solomonzelman):

not 23

2 years ago
OpenStudy (solomonzelman):

you don't add the terms before \(a_9|)

2 years ago
OpenStudy (solomonzelman):

oh, my bad

2 years ago
OpenStudy (lilymq):

so it is 1472?

2 years ago
OpenStudy (solomonzelman):

what the hell am I saying....Jhanny, i am a laborer before thee

2 years ago
OpenStudy (jhannybean):

You wrote 199 instead of 119 O_o

2 years ago
OpenStudy (solomonzelman):

i read \(a_9\) with my blind eyes.

2 years ago
OpenStudy (jhannybean):

and @LilyMQ I have no idea. No calculator here, just helping you understand the format :)

2 years ago
OpenStudy (solomonzelman):

9 is the 1st term... then it is completely off....

2 years ago
OpenStudy (solomonzelman):

(9+199)÷2 => the average term 23 = number of terms (9+199)÷2 • 23 = the sum of all terms together

2 years ago
OpenStudy (solomonzelman):

sorry for my mistake.

2 years ago
OpenStudy (lilymq):

oh, so it's 2392?

2 years ago
OpenStudy (solomonzelman):

yes, this is correct

2 years ago
OpenStudy (solomonzelman):

and this time, it is correct for real:D

2 years ago
OpenStudy (lilymq):

Yay. Okay thanks guys!

2 years ago
OpenStudy (lilymq):

Wait wait

2 years ago
OpenStudy (lilymq):

That doesn't make sense. These are the options 1,219 1,472 1,725 1,978

2 years ago
OpenStudy (lilymq):

HELPP

2 years ago
OpenStudy (solomonzelman):

the first term is 9 the last (i.e. 23rd) term is 199 are you sure about this information ?

2 years ago
OpenStudy (lilymq):

What is the sum of a 23-term arithmetic sequence where the first term is 9 and the last term is 119?

2 years ago
OpenStudy (lilymq):

119 not 199 lol

2 years ago
OpenStudy (solomonzelman):

oops my fault again, i will try to, if i can, to refrain from my mistake

2 years ago
OpenStudy (solomonzelman):

i will re-correct my post again. tnx for catching the err.

2 years ago
OpenStudy (lilymq):

haha it's okay

2 years ago
OpenStudy (solomonzelman):

(9+119)÷2 => the average term 23 = number of terms (9+119)÷2 • 23 = the sum of all terms together

2 years ago
OpenStudy (solomonzelman):

u were correct initially....

2 years ago
OpenStudy (lilymq):

o

2 years ago
OpenStudy (lilymq):

okay thank you lol

2 years ago
OpenStudy (solomonzelman):

You are like :O and I am like Oh..... my fault, lol

2 years ago
OpenStudy (solomonzelman):

thank YOU for catching it.... with me you would have gone into the forest of unnecessary wonders.

2 years ago
OpenStudy (solomonzelman):

Good luck:)

2 years ago