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?

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

AltShaka Mar 26, 2020

#1**-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.

Melody Mar 26, 2020

#3**+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 ]

CPhill Mar 27, 2020

#4**+1 **

2.

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

CPhill Mar 27, 2020

#5**+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

CPhill Mar 27, 2020

#6**+1 **

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

AltShaka Mar 27, 2020

#8**-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