Question 1030772
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Hi. this lesson is really confusing me and I need help with it. These questions are confusing me. Please help me solve these problems. 


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


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3.  b1 = 2 and bk+1 = 3bk, for k>0


    {{{b[1]}}} = 2;  {{{b[2]}}} = {{{3*b[1]}}} = 3*2 = 6, . . . 


    It is a geometric progression, first term 2, common ratio 3.

 

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


   It is a geometric progression, first term 0.75, common ratio -2.

 

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

 

6. Identify the sequence {-2, 2, -2, 2 ...} as arithmetic or geometric.  Then find the common difference or ratio as appropriate.

   
   It is a GP with the common ratio  (-1).

 

7. Identify the sequence {-5, -2, 1, 4 ...} as arithmetic or geometric.  Then find the common difference or ratio as appropriate.

 
   It is an AP with the common difference  3.


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.
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It looks like you know nothing about arithmetic and geometric progressions.


Read the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

in this site.