Find the 20th term of the series... (1 Viewer)

[haboozin]

Find the 20th term of the series...


5 - 2 + 10 - 8 + 15 -32 +20 - 128 + ...


wtf.. is ... this???

i don't get it...

its not arethmatic or geometric....

i do 4unit and maybe we skipped doing weird no-r or d series Q's ??
or maybe i've forgotten this...


anyways i have the answer, so please dont just post the answer especially if you have the book im using... please write an explanation...

 

[shafqat]

Find the 20th term of the series...


5 - 2 + 10 - 8 + 15 -32 +20 - 128 + ...


wtf.. is ... this???

i don't get it...

its not arethmatic or geometric....

i do 4unit and maybe we skipped doing weird no-r or d series Q's ??
or maybe i've forgotten this...


anyways i have the answer, so please dont just post the answer especially if you have the book im using... please write an explanation...

rearrange the series like this:

5 + 10 + 15 ...- 2 - 8 - 32...

recognise the 2 series?

 

[Trev]

It is a combination of both; it can be split into two:
5 + 10 + 15 + 20 +...
AND
-2 -8 - 32 - 128 - ...
This is only an extension 1 question.

Since there will be 10 terms of each series, geometric and arithmetic, the answer would be:

= n/2[2a + (n-1)d] + [a(rⁿ-1)]/(r-1)
= 10/2[2*5 + (10-1)*5] + [-2(4¹⁰-1]/(4-1)
= -698775
But wait, I have been foolish, and found out the sum of the first 20 terms of the series.

So now, I will answer your question lol....
The 20th term would come from the series you can identify as "-2 -8 - 32 - 128 - ...", but it would be the 10th term of that series, yet the 20th term of "5 - 2 + 10 - 8 + 15 -32 +20 - 128 + ...".
So work out the 10th term of the series "-2 -8 - 32 - 128 - ..."
T₁₀ = ar^n-1
T₁₀ = -2(4)^{10 - 1}
10th term is -524288

I hope that explains enough!

 

[haboozin]

yea, i've just never seen a question like that so i didnt think it would be possible.... but obviously it is...

sadly, its not even an ext 1 Q... its a 2unit Question from the 2unit course ...

stupid series..

 

[Trev]

yea, i've just never seen a question like that so i didnt think it would be possible.... but obviously it is...

sadly, its not even an ext 1 Q... its a 2unit Question from the 2unit course ...

stupid series..

Ahk, well then. I'm positive many of the mathematics (adv) students at my school would have no clue if a question like that came up in an exam!

 

[Jago]

that stuff is 2u? wow, that's a pretty tricky q

luckily i didn't get that in my 1/2 yrlys