SOLUTION: Consider the following sequence of figures. Figure 1 contains 5 line segments. Figure 2 contains 9 and figure three contains 13. Given that figure n contains 801 line segments,

Question 1097195: Consider the following sequence of figures.
Figure 1 contains 5 line segments.
Figure 2 contains 9 and figure three contains 13.
Given that figure n contains 801 line segments, show that n=200. already did this first part. I need to figure out how to do the part below
Find the total number of line segments in the first 200 figures.

Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.

Write the sequence 

     5,   9,    13, . . . ,  801.      (1)


Write this sequence in the reverse order:

   801,  797,  793             5        (2)


Add the numbers in pairs from the first and the second sequences. You will get the pairs

    5 + 801 = 806,
    9 + 797 = 806,

. . . . . . . . 

  801   + 5 = 806.

You have 200 pairs,  the sum of each pair is 806.


Hence, the sum of your sequence is   = 100*806 = 80600.

It is how to sum up an Arithmetic progression.

----------------
There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

RELATED QUESTIONS
1a. Consider the following sequence of figures. Figure 1 contains 5 line segments.... (answered by Edwin McCravy)

Average of 9 figures is 301 . The average of first 5 figures is 163 and average of last 5 (answered by Alan3354)

Model the following sequence of toothpick figures, Rectangles with Pluses, with... (answered by richwmiller)

1. Model the following sequence of toothpick figures, Dashes and Stars, with toothpicks... (answered by richwmiller)

Fundamental Ideas Points, Lines, and Planes Postulates and Theorems Segments,... (answered by richard1234)

What is the common ration of the sequence 1, 2/3, 3/5, 4/7, 5/9..... I've spent awhile on (answered by Alan3354,stanbon)

Figure 1 is a square with a side length of 5 units while Figure 2 is a triangle with... (answered by josgarithmetic)

average of ? figures is 301 average of first five figures is 163 and average of last 5... (answered by ikleyn)

consider the following figures circle yellow number 1 , triangle red number 2 , square... (answered by solver91311)