I don't know why I am getting the wrong answer, please help!
16. The first term of an arithmetic progression is 6 and the fifth term is 12. The progression has n terms and the sum of all the terms is 90. Find the value of n.
I will post a picture of my working out.

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

The correct answer is 8

- Nnesha

i got 8 !! :D now wait a sec i'll check ur work

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## More answers

- Nnesha

http://prntscr.com/8ig2duis it 45/n ??

- anonymous

The screenshot didn't work

- anonymous

But in the beginning I did get 45/n

- Nnesha

okay so at left side is it 45/n it's a 2nd row

- Nnesha

how did you get that ?

- anonymous

Oooh...I combined 1/2 n and 90. not like terms so I cant do that right?

- Nnesha

it's \[\frac{ 3 }{ 2}n = \frac{3n}{2}\] n isn't at the denominator

- Nnesha

ye first combine 12-3/2

- Nnesha

\[\huge\rm 90=\frac{ n(\color{Red}{12}+\frac{ 3 }{ 2 }n-\color{Red}{\frac{ 3 }{ 2} })}{ 2 }\] like terms

- anonymous

Ok. I will try again quickly.

- Nnesha

okay :=)

- anonymous

I got 7.46, Did I lose some accuracy somewhere or is that what I am meant to get?

- Nnesha

yes that's not correct

- anonymous

Awwww. Oh well. Ok should i post my working out again?

- Nnesha

yes

- welshfella

a + 4d - a = 4d = 12 - 6 = 6
so d = 3/2

- Nnesha

first multiply both sides by 2 \[\huge\rm 90 Â· 2=\frac{ n(\color{Red}{12}+\frac{ 3 }{ 2 }n-\color{Red}{\frac{ 3 }{ 2} })}{ 2 }Â· 2\]
combine 12-3/2
and then distribute parentheses by n

- anonymous

##### 1 Attachment

- anonymous

the n=9 is from the other equation

- anonymous

Oh. I think I forgot that its over 2

- Nnesha

no you didn't
you distributed the parentheses by (1/2)n

- anonymous

Yes?

- anonymous

I'm sorry, I don't really understand whaI did wrong?

- Nnesha

i know what happened t o12.25 ?? check ur 6th and 7th row

- anonymous

I was making a perfect square

- Nnesha

w|dw:1442760681511:dw|
you should add (b/2)^2 to both sides

- Nnesha

it's n^2 ** typo

- anonymous

Oh!! I forget to do that a lot >:/ Ok, third time lucky. Trying again.

- anonymous

Aaaaand I am finally getting it right!

- Nnesha

Yahooo!!

- anonymous

Thank you for your patience and for helping me so much! :D

- Nnesha

my pleasure &GREAT JOB!!
i like how u posted ur work :=) that was super cool!

- Nnesha

good luck!!

- anonymous

Thanks!

- Nnesha

o^_^o

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