Question

7) The first diagonal of Pascal's Triangle is a sequence of all 1's. The second diagonal is a sequence consisting of the positive integers, in order. The third diagonal is a sequence that can be described by the closed formula a_n = n(n+1)/2. Use this information to find a recursive formula for the sequence of terms in the fourth diagonal (1, 4, 10, 20, ...) a_{n+1} = a_n + n(n+1)/2

          7) The first diagonal of Pascal's Triangle is a sequence of all 1's. The second diagonal is a sequence consisting of the positive integers, in order. The third diagonal is a sequence that can be described by the closed formula a_n = n(n+1)/2. Use this information to find a recursive formula for the sequence of terms in the fourth diagonal (1, 4, 10, 20, ...)

a_{n+1} = a_n + n(n+1)/2

7) The first diagonal of Pascal's Triangle is a sequence of all 1's. The second diagonal is a sequence consisting of the positive integers, in order. The third diagonal is a sequence that can be described by the closed formula an = n(n+1)/2. Use this information to find a recursive formula for the sequence of terms in the fourth diagonal (1, 4, 10, 20, ...)

an+1 = an + n(n+1)/2

Added by David B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

08/07/2023

Step 1

.. 2nd diagonal: 1, 2, 3, 4, ... 3rd diagonal: 1, 3, 6, 10, ... Now, let's look at the differences between consecutive terms in each diagonal: 1st diagonal: 0, 0, 0, ... 2nd diagonal: 1, 1, 1, ... 3rd diagonal: 2, 3, 4, ... Notice that the differences in the 3rd Show more…

Show all steps

Thanks for your feedback!

The first diagonal of Pascal's Triangle is a sequence of all 1's. The second diagonal is a sequence consisting of the positive integers, in order. The third diagonal is a sequence that can be described by the closed formula an = n(n+1)/2. Use this information to find a recursive formula for the sequence of terms in the fourth diagonal (1, 4, 10, 20, ...)