Question

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.

Answer 1

The correct answer is 8

Answer 2

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

Answer 3

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

Answer 4

The screenshot didn't work

Answer 5

But in the beginning I did get 45/n

Answer 6

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

Answer 7

how did you get that ?

Answer 8

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

Answer 9

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

Answer 10

ye first combine 12-3/2

Answer 11

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

Answer 12

Ok. I will try again quickly.

Answer 13

okay :=)

Answer 14

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

Answer 15

yes that's not correct

Answer 16

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

Answer 17

yes

Answer 18

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

Answer 19

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

Answer 20

the n=9 is from the other equation

Answer 21

Oh. I think I forgot that its over 2

Answer 22

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

Answer 23

Yes?

Answer 24

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

Answer 25

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

Answer 26

I was making a perfect square

Answer 27

w
you should add (b/2)^2 to both sides