what method i need to use in solving arithmetic and geometric sequences and series?
Usually this topic requires several days or even weeks in a standard algebra or pre-Calculus course, and probably takes up several chapters in your textbook.
I don't think the little box used for text in this format is quite large enough to answer your question.
Don't you have a textbook ?
To solve arithmetic and geometric sequences and series, you need to understand and apply the appropriate formulas. Here are the methods you can use for each:
Arithmetic Sequence:
1. Formula to find the nth term (an):
an = a1 + (n - 1)d
where a1 is the first term, n is the position of a term, and d is the common difference between consecutive terms.
2. Formula to find the sum of the first n terms (Sn):
Sn = (n/2) * (a1 + an)
Geometric Sequence:
1. Formula to find the nth term (an):
an = a1 * r^(n - 1)
where a1 is the first term, r is the common ratio between consecutive terms, and n is the position of a term.
2. Formula to find the sum of the first n terms (Sn):
Sn = (a1 * (r^n - 1)) / (r - 1)
To solve a specific problem, follow these steps:
1. Identify the sequence as either arithmetic or geometric. Look for a pattern in the given terms to determine if there is a common difference (arithmetic) or a common ratio (geometric).
2. Determine the values of a1, n, d/r (common difference/ratio) given in the problem.
3. Plug the values into the appropriate formula to find the desired term or sum.
4. Simplify and compute the expression to get the final answer.
Remember, it's important to carefully read and understand the problem to ensure you use the correct formula and substitute the values correctly.