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.

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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.

Mathematics
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1 Attachment
The correct answer is 8
i got 8 !! :D now wait a sec i'll check ur work

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http://prntscr.com/8ig2duis it 45/n ??
The screenshot didn't work
But in the beginning I did get 45/n
okay so at left side is it 45/n it's a 2nd row
how did you get that ?
Oooh...I combined 1/2 n and 90. not like terms so I cant do that right?
it's \[\frac{ 3 }{ 2}n = \frac{3n}{2}\] n isn't at the denominator
ye first combine 12-3/2
\[\huge\rm 90=\frac{ n(\color{Red}{12}+\frac{ 3 }{ 2 }n-\color{Red}{\frac{ 3 }{ 2} })}{ 2 }\] like terms
Ok. I will try again quickly.
okay :=)
I got 7.46, Did I lose some accuracy somewhere or is that what I am meant to get?
yes that's not correct
Awwww. Oh well. Ok should i post my working out again?
yes
a + 4d - a = 4d = 12 - 6 = 6 so d = 3/2
first multiply both sides by 2 \[\huge\rm 90 · 2=\frac{ n(\color{Red}{12}+\frac{ 3 }{ 2 }n-\color{Red}{\frac{ 3 }{ 2} })}{ 2 }· 2\] combine 12-3/2 and then distribute parentheses by n
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the n=9 is from the other equation
Oh. I think I forgot that its over 2
no you didn't you distributed the parentheses by (1/2)n
Yes?
I'm sorry, I don't really understand whaI did wrong?
i know what happened t o12.25 ?? check ur 6th and 7th row
I was making a perfect square
w|dw:1442760681511:dw| you should add (b/2)^2 to both sides
it's n^2 ** typo
Oh!! I forget to do that a lot >:/ Ok, third time lucky. Trying again.
Aaaaand I am finally getting it right!
Yahooo!!
Thank you for your patience and for helping me so much! :D
my pleasure &GREAT JOB!! i like how u posted ur work :=) that was super cool!
good luck!!
Thanks!
o^_^o

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