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
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