which is the easies,t Arithmetic Series or a Geometric Series? and why?

What is the easiest for you?

find all the numbers less then 100 that are the product of exactly three different prime numbers.

To determine whether an Arithmetic Series or a Geometric Series is easier, let's first define these two types of series:

1. Arithmetic Series: In an arithmetic series, each term is obtained by adding a constant difference, called the common difference, to the previous term. For example, 2, 5, 8, 11, ... is an arithmetic series with a common difference of 3.

2. Geometric Series: In a geometric series, each term is obtained by multiplying the previous term by a constant ratio, called the common ratio. For example, 3, 6, 12, 24, ... is a geometric series with a common ratio of 2.

Now, let's compare these two series in terms of ease:

1. Arithmetic Series: Calculating the terms of an arithmetic series is relatively straightforward. Once you know the first term and the common difference, you can easily find any term in the series using the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term in the series, and d is the common difference. This formula allows for quickly determining any term in the series without requiring complicated calculations.

2. Geometric Series: Calculating the terms of a geometric series can involve more complex calculations compared to an arithmetic series. To find any term in a geometric series, you can use the formula: an = a1 * r^(n-1), where an is the nth term, a1 is the first term, n is the position of the term in the series, and r is the common ratio. Though this formula is straightforward to use, raising a number to a power, especially for higher positions in the series, can become more challenging and time-consuming.

Based on these observations, arithmetic series are generally considered easier to work with because the formulas involved are simpler and require less computation compared to geometric series. However, the ease of solving either type of series can also depend on personal preference, mathematical ability, and the specific problem at hand.