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(52792)   (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.
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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.
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