Question

For each of the following sequences, determine an algebraic formula, similar to Exercise #4, that defines the sequence. a 5, 10, 15, 20, … b 3, 9, 27, 81, … c 1/2 , 2/3 , 3/4 , 4/5 ,..

Answer 1

The algebraic formulas for the provided sequences are: a(n) = 5n for the arithmetic sequence, b(n) = 3^n for the geometric sequence, and c(n) = n/(n+1) for the fraction sequence.

Step-by-step explanation:

The question asks for algebraic formulas for three different sequences:

• Sequence a is an arithmetic sequence, where each term increases by 5. To find the nth term of this sequence, we use an arithmetic sequence formula: a(n) = 5n.
• Sequence b is a geometric sequence, where each term is multiplied by 3 from the previous term. The nth term can be found using the geometric sequence formula: b(n) = 3^n.
• Sequence c is a sequence of fractions where the numerator is 1 less than the denominator. The nth term of this sequence is: c(n) = n/(n+1).