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#1 2016-04-28 14:47:12

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Sequences & Series

For questions 3-5, find the first 4 terms and the 8th term of the recursively-defined sequence.

3.  b1 = 2 and bk+1 = 3bk, for k>0



4. v1 = 0.75 and vn = (-2)vk-1 for n>1



5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0



8. The third and sixth terms of a geometric sequence are -75 and -9375 respectively.  Find the first term, the common ratio, and an explicit rule for the nth term.

For problems 9 and 10, write each sum using summation notation.

9.2 + 5 + 8 + 11 + ... + 29


10. 6 - 12 + 24 - 48 + ...

12. Find the sum of the geometric sequence 42, 7/6, ..., 42(1/6)^8 


For problems 13 and 14, find the sum of the first n terms of the sequence.  The sequences are either arithmetic or geometric.

13.  -1, 11, -121, ...; n = 9


14. 14, 8, 2,...; n=9

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#2 2016-04-28 14:59:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences & Series

Hi;

3) Your notation is bad. It is written like this: b(1) = 2 and b(k+1) = 3b(k).

The first 8 terms of this sequence is 2, 6, 18, 54, 162, 486, 1458, 4374,..., so the first 4 are 2, 6, 18, 54 and the 8th term is 4374.

I have go offline for a while I will see you later.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-04-28 15:00:39

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Sequences & Series

Okay, thank you for your help tonight. I'll keep a look out for your posts tomorrow!

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#4 2016-04-28 15:43:36

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: Sequences & Series

Hey (:

Arithmetic series:



Geometric series:


Last edited by Relentless (2016-04-28 17:27:21)

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#5 2016-04-28 16:01:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences & Series

Hi;

9,10 and 12 have already been done for you earlier.

13) -196495641

14) - 90


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2016-04-29 00:37:06

Lpravia020614
Member
Registered: 2015-11-03
Posts: 35

Re: Sequences & Series

When was 9, 10, 12 done ? i didn't see them.

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#7 2016-04-29 04:13:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences & Series


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2016-04-29 18:31:27

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: Sequences & Series

Hi bobbym, our answers for 12. differ in the numerator and i cannot reproduce yours.

12. The terms are

Adding those directly, we get my answer

Last edited by Relentless (2016-04-29 18:38:43)

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#9 2016-04-29 18:44:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Sequences & Series

Different sequences.

The one she had before looked like this

12. Find the sum of the geometric sequence 42, 7 , 7/6,...,42(1/6)^8


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#10 2016-04-29 19:03:39

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: Sequences & Series

Oh ok! In that case I agree. (:

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