arithmetic series Urgent help!!!!

Hi Guyssss,

Please help - Ive been stuck on this for like 20 mins. I know i should be spending more time but ive given it all and i really have to move on to geometric sequences and series next. So i will attach the question and whatever working out i managed to get to.

So, since a circle is 360 degrees and it gets divided by 12 that would mean the sum of the 12 terms equals 360. --> S12 = 12/2 * (2U1 +(12-1)*d) = 360 ==> 6(2U1+11d) = 360 ==> 12U1 + 66d = 360. Thats all I have managed to come up with, I'm positive that this is correct so far but I might be wrong. Thanks - really appreciate any help!

the answer is 20 degrees btw

Easy Math Editor

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Comments

Yes, you're going on the right path. Look at the second information given in the problem:

The angle of the largest sector is twice the angle of the smallest sector.

This gives $\dfrac{U_1 + 11d}{U_1} = 2$ , which gives a second equation in terms of $U_1$ and $d$ . After then it's a simple system of linear equations in 2 variables.

Hope this was helpful.

Tapas Mazumdar - 3 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$