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

- LilyMQ

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

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- LilyMQ

Is it 1472? That's what I got

- Jhannybean

First define what an arithmetic sum is.

- SolomonZelman

i think you are a little off

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## More answers

- LilyMQ

So it's wrong?

- SolomonZelman

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

- SolomonZelman

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

- LilyMQ

is it 1456?

- Jhannybean

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

- LilyMQ

okay

- SolomonZelman

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

- Jhannybean

Yeah I just reread it haha

- SolomonZelman

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

- SolomonZelman

alright....

- SolomonZelman

1456 is right....

- SolomonZelman

1456 apples, jk

- Jhannybean

but whats with the multiplication?

- LilyMQ

then what?

- SolomonZelman

multiplication ?

- SolomonZelman

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

- Jhannybean

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

- SolomonZelman

not 23

- SolomonZelman

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

- SolomonZelman

oh, my bad

- LilyMQ

so it is 1472?

- SolomonZelman

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

- Jhannybean

You wrote 199 instead of 119 O_o

- SolomonZelman

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

- Jhannybean

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

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

sorry for my mistake.

- LilyMQ

oh, so it's 2392?

- SolomonZelman

yes, this is correct

- SolomonZelman

and this time, it is correct for real:D

- LilyMQ

Yay. Okay thanks guys!

- LilyMQ

Wait wait

- LilyMQ

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

- LilyMQ

HELPP

- SolomonZelman

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

- LilyMQ

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

- LilyMQ

119 not 199 lol

- SolomonZelman

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

- SolomonZelman

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

- LilyMQ

haha it's okay

- SolomonZelman

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

- SolomonZelman

u were correct initially....

- LilyMQ

o

- LilyMQ

okay thank you lol

- SolomonZelman

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

- SolomonZelman

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

- SolomonZelman

Good luck:)

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