Question

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

Answer 1

Is it 1472? That's what I got

Answer 2

First define what an arithmetic sum is.

Answer 3

i think you are a little off

Answer 4

So it's wrong?

Answer 5

\(\large\color{black}{ \displaystyle a_9=9 }\)
\(\large\color{black}{ \displaystyle a_{23}=119 }\)

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

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

Answer 6

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

Answer 7

is it 1456?

Answer 8

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

Answer 9

okay

Answer 10

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

Answer 11

Yeah I just reread it haha

Answer 12

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

Answer 13

alright....

Answer 14

1456 is right....

Answer 15

1456 apples, jk

Answer 16

but whats with the multiplication?

Answer 17

then what?

Answer 18

multiplication ?

Answer 19

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

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

Answer 20

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

Answer 21

not 23

Answer 22

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

Answer 23

oh, my bad

Answer 24

so it is 1472?

Answer 25

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

Answer 26

You wrote 199 instead of 119 O_o

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

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

Answer 31

sorry for my mistake.

Answer 32

oh, so it's 2392?

Answer 33

yes, this is correct

Answer 34

and this time, it is correct for real:D

Answer 35

Yay. Okay thanks guys!

Answer 36

Wait wait

Answer 37

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

1,472

1,725

1,978

Answer 38

HELPP

Answer 39

the first term is 9
the last (i.e. 23rd) term is 199

are you sure about this information ?

Answer 40

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

Answer 41

119 not 199 lol

Answer 42

oops my fault again,
i will try to, if i can,

to refrain from my mistake

Answer 43

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

Answer 44

haha it's okay

Answer 45

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

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

Answer 46

u were correct initially....

Answer 47

o

Answer 48

okay thank you lol

Answer 49

You are like :O and I am like Oh.....

my fault, lol

Answer 50

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

Answer 51

Good luck:)