# Unit 8 Project Inferences And Conclusions From Data Project

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Algebra
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Unit 8 Project
1. Find the next five terms of the arithmetic sequence 42, 37, 32…
Solution: the next five terms are: 27, 22, 17, 12, and 7
2. Find the 24th term of an arithmetic sequence for which a
1
= 2 and d = 6
Solution:
 

 
3. Find the three arithmetic means between -4 and 16
Solution:
Assume the arithmetic means to be: a, b, c, so the arithmetic sequence will
be: -4, a, b, c, 16


 
  
  
    

  
 

Then the three arithmetic means are: 1, 6, and 11
4. Find the sum of the arithmetic series for which a
1
= 7, n = 31, and a
n
= 127.
Solution:
The sum of the arithmetic series

  

5. Find the next three terms of the geometric sequence 81, 27, 9
Solution: the next three terms are: 
6. Find the eighth term of the geometric sequence for which a
1
= 5 and r = -2.
Solution:

 




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7. Find two geometric means between 7 and 189
Solution: Assume the two geometric means are x and y
Then the geometric sequence will be: 7, x, y, 189



 
 



  
  
 
Then the two geometric means are: 21 and 63
8. Find the sum of the geometric series for which a
1
= 125, r = , and n = 4
Solution:
The sum of the geometric series





9. Find the sum of the series:
 


Solution:
This is arithmetic series:
Where: a
1
when: K=3 then:
  
a
n
when: K=15 then:
   

   
The sum of the arithmetic series

  

10. Find the sum of the series: 91 + 85 + 79 ++ (29)
Solution:
This is arithmetic series:
Where:

, 
 
  
 
 

   
The sum of the arithmetic series




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Unit 8 Project 1. Find the next five terms of the arithmetic sequence 42, 37, 32… Solution: the next five terms are: 27, 22, 17, 12, and 7 2. Find the 24th term of an arithmetic sequence for which a1 = 2 and d = 6 Solution: 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑 = 2 + (24 − 1) × 6 = 𝟏𝟒𝟎 3. Find the three arithmetic means between -4 and 16 Solution: Assume the arithmetic means to be: a, b, c, so the arithmetic sequence will be: -4, a, b, c, 16 𝑎1 = −4, 𝑎5 = 16 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑 ∴ 𝑎5 = 𝑎1 + (5 − 1)𝑑 20 ∴ 16 = −4 + 4𝑑 ∴ 4𝑑 = 16 + 4 = 20 ∴ 𝑑 = =5 4 ∴ 𝑎 = −4 + 𝑑 = −4 + 5 = 1 ∴𝑏 = 𝑎+𝑑 = 1+5=6 ∴ 𝑐 = 6 + 5 = 11 Then the three arithmetic means are: 1, 6, and 11 4. Find the sum of the arithmetic series for which a1 = 7, n = 31, and an= 127. Solution: 𝑛 31 The sum of the arithmetic series= (𝑎1 + 𝑎𝑛 ) = × (7 + 127) = 𝟐𝟎𝟕𝟕 2 2 5. Find the next three terms of the geometric sequence 81, 27, 9… Solution: the next three terms are: 𝟑, 𝟏, 𝟏 𝟑 6. Find the eighth term of the geometric sequence for which a1 = 5 and r = -2. Solution: 𝑎𝑛 = 𝑎1 × 𝑟 (𝑛−1) = 5 × (−2)(8−1) = 5 × (−2)7 = −𝟔𝟒𝟎 7. Find two geometric means between 7 and 189 Solution: Assume the two geometric means are x and y Then the geometric sequence will be: 7, x, y, 189 𝑎1 = 7, 𝑎4 = 189 𝑎𝑛 = 𝑎1 × 𝑟 (𝑛−1) ∴ 𝑎4 = 𝑎1 × 𝑟 (4−1) 1 ...
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