SOLUTION: Rewrite this series in sigma notation: -4 + -1 + 8 + 23 + 44 + 71 + 104

Algebra.Com
Question 1003331: Rewrite this series in sigma notation:
-4 + -1 + 8 + 23 + 44 + 71 + 104
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
First we figure out the pattern:

-4 + -1 + 8 + 23 + 44 + 71 + 104
         
 start with -4  
  -4 +  3 = -1
  -1 +  9 =  8
   8 + 15 = 23
  23 + 21 = 44
  44 + 27 = 71
  71 + 33 = 104

We are adding an odd multiple of 3 each time.
So we could write it this way:

   start with -4  
  -4 +  3*1 = -1
  -1 +  3*3 =  8
   8 +  3*5 = 23
  23 +  3*7 = 44
  44 +  3*9 = 71
  71 + 3*11 = 104

We start with this

-4 + -1 + 8 + 23 + 44 + 71 + 104

and go through a bunch of substitutions using the above list

-4 + -1 + 8 + 23 + 44 + 71 + 1*(71 + 3*11)

-4 + -1 + 8 + 23 + 44 + 71 + 71 + 1*3*11

-4 + -1 + 8 + 23 + 44 + 2*71 + 1*3*11

-4 + -1 + 8 + 23 + 44 + 2*(44 +  3*9) + 1*3*11

-4 + -1 + 8 + 23 + 44 + 2*44 +  2*3*9 + 1*3*11

-4 + -1 + 8 + 23 + 3*44 +  2*3*9 + 3*11

-4 + -1 + 8 + 23 + 3*(23 +  3*7) +  2*3*9 + 1*3*11

-4 + -1 + 8 + 23 + 3*23 +  3*3*7 +  2*3*9 + 1*3*11

-4 + -1 + 8 + 4*23 +  3*3*7 +  2*3*9 + 3*11

-4 + -1 + 8 + 4*(8 +  3*5) +  3*3*7 +  2*3*9 + 1*3*11

-4 + -1 + 8 + 4*8 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + -1 + 5*8 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + -1 + 5*(-1 +  3*3) +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + -1 + 5*(-1) +  5*3*3 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + 6*(-1) +  5*3*3 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + 6*(-4 +  3*1) +  5*3*3 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-4 + 6*(-4) +  6*3*1 +  5*3*3 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

7*(-4) +  6*3*1 +  5*3*3 +  4*3*5 +  3*3*7 +  2*3*9 + 1*3*11

-28 + 3*(6*1 +  5*3 +  4*5 +  3*7 +  2*9 + 1*11)

Using the formula for the nth term of an arithmetic sequence 

                        

The sequence 6,5,4,3,2,1 has kth term 6+(k-1)(-1) = 6-k+1 = 7-k

The sequence 1,3,5,7,9,11 has kth term 1+(k-1)(2) = 1+2k-2 = 2k-1

In summation form is




Edwin
RELATED QUESTIONS

rewrite series as sigma notation 1) 25+36+49+64+81 2)... (answered by Edwin McCravy)
rewrite series as sigma notation 1)... (answered by math_helper)
Write the series in sigma notation: 1 + 2 + 3 + ... + 99 2 3 4... (answered by ewatrrr)
How to write the series in sigma/summation notation? -2 + 1 + 4 + 7 + ... +... (answered by FrankM)
Write this in sigma notation, please??... (answered by hovuquocan1997,MathLover1)
could you show me how to write the series 1+(1/2)+(1/4)........(1/4096) in sigma... (answered by stanbon)
How do I use the sigma notation to express the series : 2+1+1/2+1/4+1/8.............. (answered by Fombitz)
0+1+2+3+4+5+6+7+8+9 what is the sigma notation for the... (answered by Edwin McCravy)
0+1+2+3+4+5+6+7+8+9 what is the sigma notation for the series? (answered by Edwin McCravy,palanisamy)