Question

Discrete Mathematics

a) Find a closed formula (rule) that generates the following sequence

A: A=(3,6,11,18,27,…) b) Find a closed formula (rule) that generates the following sequence

B: B= (2/1 , 4/2, 8/3. 16/4, 32/5......) c) Find a closed formula (rule) that generates the following sequence

D: D= (-1,1, -1,1, -1,1, -1,1, -1,.......) d) Find a closed formula (rule) that generates the following sequence

E: E=(1/2, 1/3, 1/4, 1/5, 1/6.......) Please note that each question is asking for a mathematical rule or formula that generates the given sequences. Your answers should provide a formula in terms of n or some variable, where n represents the position in the sequence.

Answer 1

The closed formulas for the given sequences are An = 3 + (n-1)(2), Bn = (2 * n)/(n+1), Dn = (-1)n+1, and En = 1/n.

Step-by-step explanation:

a) To find a closed formula for sequence A, observe that the sequence increases by 3, then 5, then 7, and so on. This means that the nth term of the sequence can be calculated using the formula: An = 3 + (n-1)(2).

b) For sequence B, notice that the numerator doubles with each term, while the denominator increases by 1. So, the nth term of the sequence can be expressed as: Bn = (2 * n)/(n+1).

c) The pattern in sequence D repeats the numbers -1 and 1. Since the sequence alternates every term, we can use the formula: Dn = (-1)n+1.

d) Sequence E consists of the reciprocals of the positive integers. So, the nth term can be represented as: En = 1/n.