4) Below, see the first few figures in a sequence along with their number (in the first set of square numbers, yousee the term or figure number along with the term). Determine the number of dots or squares (term) in thenext four figures for each, and – if possible - in the nth figure. (Generalize).a) Square numbersorfigure34149.162536b) Triangular Numbersfigure 1figure 2figure 3figure 4or110ORc) Pentagonal numbersfigure 1figure 2figure 3figure 41122236127[36]O O 0 0

Name: 4) Below, see the first few figures in a sequence along with their nu
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Description: 4) Below, see the first few figures in a sequence along with their number (in the first set of square numbers, yousee the term or figure number along with the term). Determine the number of dots or squares (term) in thenext four figures for each, an

Answered: 4) Below, see the first few figures in…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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4) Below, see the first few figures in a sequence along with their number (in the first set of square numbers, you
see the term or figure number along with the term). Determine the number of dots or squares (term) in the
next four figures for each, and – if possible - in the nth figure. (Generalize).
a) Square numbers
or
figure
3
4
1
4
9.
16
25
36
b) Triangular Numbers
figure 1
figure 2
figure 3
figure 4
or
1
10
OR
c) Pentagonal numbers
figure 1
figure 2
figure 3
figure 4
1
12
22
36
127
[36]
O O 0 0

Expert Solution

Step 1 : b) Square

$S q u a r e n u m b e r s : n = f i g u r e n u m b e r s = n u m b e r o f s q u a r e s W h e n n = 1, t h e n s = 1 o r 1^{2} W h e n n = 2, t h e n s = 4 o r 2^{2} W h e n n = 3, t h e n s = 9 o r 3^{2} W h e n n = 4, t h e n s = 16 o r 4^{2} W h e n n = 5, t h e n s = 25 o r 5^{2} W h e n n = 6, t h e n s = 36 o r 6^{2} . . . W h e n n = m, t h e n s = m * m o r m^{2}$

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