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107
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avatar+416 

1. How many terms of the arithmetic sequence 88, 85, 82, . . . appear before the number -17 appears?

 

2.The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?

 

3.The lattice shown is continued for 100 rows. What will be the third number in the 100th row?

\(\[\begin{array}{r|ccccccc} \text{Row } 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \text{Row } 2 & 8 & 9 & 10 & 11 & 12 & 13 & 14 \\ \text{Row } 3 & 15 & 16 & 17 & 18 & 19 & 20 & 21 \\ \text{Row } 4 & 22 & 23 & 24 &25 & 26 & 27 & 28 \\ \end{array}\]\)

 Mar 26, 2020
 #1
avatar+109509 
-1

Please just post one question per post.  

Besides other reasons you will cut down on the number of people that may answer if you annoy people. 

Asking multiple questions on one post annoys me.

 Mar 26, 2020
 #2
avatar+416 
+1
Sorry lol
 
 Mar 26, 2020
 #7
avatar+109509 
0

Do you think it is wise to vote me down AltShaka?  

I was just pointing out the obvious.

Melody  Mar 27, 2020
 #3
avatar+111321 
+1

1)   We have  that  the common difference between terms  is  - 3 .....so....

 

88  -  3 (n - 1)  = -17      simplify

 

88 - 3n + 3  =  -17

 

91  - 3n  =  - 17   subtract  91  from both sides

 

-3n = -108      divide by  -3

 

n =   36     [ -17 will be the  36th term ]

 

 

cool cool cool

 Mar 27, 2020
 #4
avatar+111321 
+1

2.

 

See here  :  https://web2.0calc.com/questions/the-fifth-term-of-an-arithmetic-sequence-is-9-and_4

 

 

cool cool cool

 Mar 27, 2020
 #5
avatar+111321 
+1

3)

 

Not too much  here

 

Note  that  the third  number  in each row follows  the pattern  3,10, 17, 24, etc.

 

The common difference is  7....so....

 

 

3  + 7(n - 1)    gives us the  3rd number in each row  for any row, n

 

So 

 

3 + 7(100 - 1)  =

 

3 + 700 - 7   = 

 

700 - 4     =

 

696  =  3rd number in row 100

 

 

cool cool cool

 Mar 27, 2020
 #6
avatar+416 
+1

Hmm cphill how did you s***w up on the first one?? Its 35 since -17 is the 36th!

 Mar 27, 2020
 #8
avatar+1956 
-2

Anyone can mess up, even CPhill! That was kinda mean, and I think it would be nice if you would apologize.

 

Best,

CalTheGreat  Mar 28, 2020

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