## LilyMQ one year ago What is the sum of a 23-term arithmetic sequence where the first term is 9 and the last term is 119?

1. LilyMQ

Is it 1472? That's what I got

2. anonymous

First define what an arithmetic sum is.

3. SolomonZelman

i think you are a little off

4. LilyMQ

So it's wrong?

5. SolomonZelman

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

6. SolomonZelman

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

7. LilyMQ

is it 1456?

8. anonymous

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

9. LilyMQ

okay

10. SolomonZelman

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

11. anonymous

Yeah I just reread it haha

12. SolomonZelman

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

13. SolomonZelman

alright....

14. SolomonZelman

1456 is right....

15. SolomonZelman

1456 apples, jk

16. anonymous

but whats with the multiplication?

17. LilyMQ

then what?

18. SolomonZelman

multiplication ?

19. SolomonZelman

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

20. anonymous

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

21. SolomonZelman

not 23

22. SolomonZelman

you don't add the terms before $$a_9|) 23. SolomonZelman oh, my bad 24. LilyMQ so it is 1472? 25. SolomonZelman what the hell am I saying....Jhanny, i am a laborer before thee 26. anonymous You wrote 199 instead of 119 O_o 27. SolomonZelman i read \(a_9$$ with my blind eyes.

28. anonymous

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

29. SolomonZelman

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

30. SolomonZelman

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

31. SolomonZelman

sorry for my mistake.

32. LilyMQ

oh, so it's 2392?

33. SolomonZelman

yes, this is correct

34. SolomonZelman

and this time, it is correct for real:D

35. LilyMQ

Yay. Okay thanks guys!

36. LilyMQ

Wait wait

37. LilyMQ

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

38. LilyMQ

HELPP

39. SolomonZelman

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

40. LilyMQ

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

41. LilyMQ

119 not 199 lol

42. SolomonZelman

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

43. SolomonZelman

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

44. LilyMQ

haha it's okay

45. SolomonZelman

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

46. SolomonZelman

u were correct initially....

47. LilyMQ

o

48. LilyMQ

okay thank you lol

49. SolomonZelman

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

50. SolomonZelman

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

51. SolomonZelman

Good luck:)