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1. If t, and s, are trinagular and square numbers, respectively, show that 8t, +1= s2n+1- 2. A pentagonal number p, is defined by n(3n – 1) Pn a. Determine and illustrate the first four pentagonal numbers. b. Define pn recursively.

1. If t, and s, are trinagular and square numbers, respectively, show that 8t, +1= s2n+1- 2. A pentagonal number p, is defined by n(3n – 1) Pn a. Determine and illustrate the first four pentagonal numbers. b. Define pn recursively.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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V. Do as indicated. 1. If and Sn are trinagular and square numbers, respectively, show that 8t, +1= s2n+1- 2. A pentagonal number p, is defined by n(3n – 1) Pn = 2 a. Determine and illustrate the first four pentagonal numbers. b. Define p, recursively. 2 3. Show that tŋ-1+ Sn = Pn: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square. 5. A pentagonal pyramidal number P, can be determined using the dot representations of pentagonal number, the same way with the triangular and square pyramidal numbers. Determine the first five pentagonal pyramidal numbers.
Transcribed Image Text:V. Do as indicated. 1. If and Sn are trinagular and square numbers, respectively, show that 8t, +1= s2n+1- 2. A pentagonal number p, is defined by n(3n – 1) Pn = 2 a. Determine and illustrate the first four pentagonal numbers. b. Define p, recursively. 2 3. Show that tŋ-1+ Sn = Pn: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square. 5. A pentagonal pyramidal number P, can be determined using the dot representations of pentagonal number, the same way with the triangular and square pyramidal numbers. Determine the first five pentagonal pyramidal numbers.
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