# C2 may 2005- Arithmetic sequencesWatch

Thread starter 7 years ago
#1
I am lost on a C2 question based on arithmetic sequences.. If I could have some assistance it would me much appreciated.

"There is a flowerhead at the end of each stem of a plant. The next year, each flowerhead is replaced by three stems and flowerheads" ( If you can imagine in year one, just one stem with one flowerhead, then year two replace that flowerhead with three new stems with a flowerhead at the end of those stems, and year three replace those flowerheads each with three stems ( total of 9 new stems) and have a flowerhead on each. Hard explain as there is a diagram in the paper.

The question is:

"The total number of stems in year 2 is 4, ( that is, 1 old one and 3 new ones) . Similarly, the total number of stems in year 3 is 13, ( that is 1 + 3 + 9 )"

"show that the total number of stems in year n is given by ((3^n)-1) / 2"

Am I right in that you use the n/2( 2a + (n-1)d) equation, where a =2 , and d= 3^n-1? But from there I cannot get the given equation

Any help would be much appreciated, thanks!
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7 years ago
#2
That's not an arithmetic sequence since the difference between terms isn't equal.

Try looking at geometric series instead.
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7 years ago
#3
Its geometric series at C2
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7 years ago
#4
Completely different topic required: check geometric series.
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Thread starter 7 years ago
#5
Ah of course, but I can't find the common ratio r of the sequence: 1 , 4 , 13 , 40 , 121..... only that it is ( x3 + 1)?
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