Since we can write a square number as the sum of two consecutive triangular numbers, we can write a pentagonal number in terms of triangular numbers. What is the nth pentagonal number in terms of triangular numbers? Write a recursive formula to represent pentagonal numbers in terms of triangular numbers. Use your results to write a formula to determine the nth pentagonal number in terms of n.
Added by Daniela P.
Step 1
We know that a square number can be written as the sum of two consecutive triangular numbers. Since a pentagonal number is the sum of a square number and a triangular number, we can write P_n as: P_n = S_n + T_n where S_n is the nth square number. We can rewrite Show more…
Show all steps
Close
Your feedback will help us improve your experience
Naresh Bagrecha and 81 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Madhur L.
Show that a pentagonal number is the sum of a square number and a triangular number. How does the square number relate to the corresponding triangular number? That is, which square number and which triangular number appear in each pentagonal number? Write a recursive formula to represent each pentagonal number in terms of a square number and a triangular number.
Triangular Numbers A triangular number is a term of the sequence $$ u_{1}=1 \quad u_{n+1}=u_{n}+(n+1) $$ Write down the first seven triangular numbers.
Rukhmani J.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD