18. Pentagonal numbers n(3n-1) a.) The formula for Pentagonal numbers is P = fifth Pentagonal number. Show your work. Use the formula to find Ps, the b.) Pentagonal numbers can be drawn to look like pentagons, or like houses! Write the next pentagonal number and draw the corresponding picture. Make sure your picture matches what you found in part al P1= 1 P2=5 P3= 12 P= 22 Ps = c.) Show that the P2, P3 , P4 and Ps can be split into two shapes, a triangular number and a square number. Hint: the square is the bottom of the house and the triangle is the roof! Circle each part! The first one has been done for you. Ti Sz P2=5 P3= 12 P4= 22 P5 d.) Complete the table below. Pentagonal number | The same as adding the triangular and square numbers.... P2= 5 P3 = 12 P4 = 22 Ps = T1+ S2 e.) Write the general formula, with the correct subscripts, using the variable, n. Pn = T2+ S?

18. Pentagonal numbers n(3n-1) a.) The formula for Pentagonal numbers is P = fifth Pentagonal number. Show your work. Use the formula to find Ps, the b.) Pentagonal numbers can be drawn to look like pentagons, or like houses! Write the next pentagonal number and draw the corresponding picture. Make sure your picture matches what you found in part al P1= 1 P2=5 P3= 12 P= 22 Ps = c.) Show that the P2, P3 , P4 and Ps can be split into two shapes, a triangular number and a square number. Hint: the square is the bottom of the house and the triangle is the roof! Circle each part! The first one has been done for you. Ti Sz P2=5 P3= 12 P4= 22 P5 d.) Complete the table below. Pentagonal number | The same as adding the triangular and square numbers.... P2= 5 P3 = 12 P4 = 22 Ps = T1+ S2 e.) Write the general formula, with the correct subscripts, using the variable, n. Pn = T2+ S?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

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18. Pentagonal numbers
п(Зп-1)
a.) The formula for Pentagonal numbers is Pn
Use the formula to find Ps, the
fifth Pentagonal number. Show your work.
b.) Pentagonal numbers can be drawn to look like pentagons, or like houses! Write the
next pentagonal number and draw the corresponding picture. Make sure your
picture matches what you found in part a!
P1= 1
P2=5
P3= 12
P4= 22
P5 =
c.) Show that the P2, P3 , P4 and Ps can be split into two shapes, a triangular number
and a square number. Hint: the square is the bottom of the house and the triangle
is the roof! Circle each part! The first one has been done for you.
Ti
Sz
P2=5
P3= 12
P4= 22
P5
d.) Complete the table below.
Pentagonal number | The same as adding the triangular and square numbers....
P2= 5
P3 = 12
Ti+ S2
P4 = 22
P5 =
e.) Write the general formula, with the correct subscripts, using the variable, n.
Pn = T? + S?

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