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#1 2016-05-06 14:02:34

90sginger
Member
Registered: 2016-04-20
Posts: 19

Sequences and Series help again!

Hi, this is my last algebra lesson and I need to finish this class before May 12th, please help me! I did the questions that I could the best I could. Here is what I really need help with it! I appreciate it!

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
My answer was:
b(1) = 2
b(2) = 3*b1 = 3*2 = 6
b(3) = 3*b2 = 3*6 = 3^2*2 = 9*2 = 18
b(4) = 3*b3 = 3*3^2*2 = 3^3*2 = 54
b(8) = 3^4*2 = 81*2 = 162

My teacher said 8th term not corect, but the others are!

4. v1 = 0.75 and vn = (-2)vk-1 for n>1
My answer was:
v(1) = 3/4
v(2) = -2(3/4)
v(3) = (-2)^2(3/4) = 3
v(4) = (-2)^3(3/4) = -6
v(8) = (-2)^6(3/4) = 48

She said: 2nd and 8th term incorrect

5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0
My answer was:
c(1) = 2
c(2) = -1
c(3) = 2+-1 = 1
c(4) = -1 + 1 = 0
c(8) = c(6) + c(5) = [c(4)+c(5)] + c(5) = [0+1+1] = 2

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.
She said: #8 is tells you the 3rd term is -75 and the 6th term is -9375.  You need to figure out what the 1st term is...and how to get from 1 to the next!

12. Find the sum of the geometric sequence
http://www.sc.whitmoreschool.org/sec/st … age107.gif

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 2016-05-06 14:10:56

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

Re: Sequences and Series help again!

Hi;

3) 162 is the b(5), b(8) is 4374

4) The question has a mistake in the wording.

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

You probably mean v(k) = -2 v(k-1)...


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 2016-05-06 14:19:33

90sginger
Member
Registered: 2016-04-20
Posts: 19

Re: Sequences and Series help again!

bobbym wrote:

Hi;

3) 162 is the b(5), b(8) is 4374

4) The question has a mistake:

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

You probably mean v(k) = -2 v(k-1)...

That was how the question was written but yeah I think that was what it means.

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#4 2016-05-06 14:22:02

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

Re: Sequences and Series help again!

4. v1 = 0.75 and vn = (-2)vk-1 for n>1
My answer was:
v(1) = 3/4
v(2) = -2(3/4)
v(3) = (-2)^2(3/4) = 3
v(4) = (-2)^3(3/4) = -6
v(8) = (-2)^6(3/4) = 48

Your v(2) is correct, your teacher is incorrect.

Your v(8) is incorrect, v(8) = -96

-----------------------------------------------------------------------

For 5)

c(8) = c(6) + c(5) = [c(4)+c(5)] + c(5) = [0+1+1] = 2

The correct answer is,

c(8) = c(7) + c(6)  = 3

------------------------------------------------------------------------

For 8)

The first term is -3 and the general term is

-------------------------------------------------------------------------

For 12)

-------------------------------------------------------------------------

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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