Series question from challenge exercise 8 (1 Viewer)

Thylacine · Feb 12, 2013

Find the sum of the first 20 terms of the series
5 - 2 + 10 - 8 + 15 - 32 + 20 - 128 + ....

asianese · Feb 12, 2013

There are two series going on here.

$S_1 = 5+10+15+20+\cdots \Rightarrow AP: a=5, d=5.\\ S_1=\frac{n}{2}(2a+(n-1)d)\\=\frac{10}{2}(2\times5+(10-1)\times5)\\=275\\ \\ S_2 = -2-8-32-128-\cdots \Rightarrow GP: a=-2, r=4.\\ S_2=\frac{a(1-r^n)}{1-r}\\=\frac{-2(1-4^{10})}{1-4}\\=-699050\\ \therefore S_{TOTAL} = 275-699050 = -698775$

Since we split the series into two, we only need the first 10 from each series to make up the whole thing.

Thylacine · Feb 13, 2013

Thankyou so much.
This question was driving me crazy.
I was trying to find the formula that produced the series.

Your way is much simpler thanks again.

asianese · Feb 13, 2013

Not a problem

This question was all about pattern recognition (which is an important skill to develop!).

Drongoski · Feb 13, 2013

asianese said:
Not a problem

This question was all about pattern recognition (which is an important skill to develop!).

Good point. As you get into more and more advanced maths, it becomes increasingly about structures, patterns and decreasingly about numbers and numerical computation.

Series question from challenge exercise 8 (1 Viewer)

Thylacine

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asianese

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Thylacine

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asianese

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Drongoski

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