Question

Discrete Mathematics

A) Find the closed formula generating the following arithmetic sequences: a) N={1,2,3,4,5,…}
b) P={4,2,0,−2,−4,−6,−8,…} (Note: It was not specified that arithmetic sequences needed to be found for these patterns, so this question asks for the closed formulas for the sequences.)

Answer 1

For sequence N, the closed formula is a_n = n, while for sequence P, the closed formula is a_n = 4 - 2n.

Step-by-step explanation:

a) The arithmetic sequence N = {1, 2, 3, 4, 5, ...} can be represented by the closed formula an = n, where n is the position of the term in the sequence. For example, a1 = 1, a2 = 2, a3 = 3, and so on.

b) The arithmetic sequence P = {4, 2, 0, -2, -4, -6, -8, ...} can be represented by the closed formula an = 4 - 2n, where n is the position of the term in the sequence. For example, a1 = 4, a2 = 2, a3 = 0, a4 = -2, and so on.