superconduct said:Homework Statement
Given successive terms of numbers starting from the 1st term:
11, 21, 35, 53, 75, 101,...
What is the general expression of the nth term? where n is positive integer
Homework Equations
/The Attempt at a Solution
Can't find a good attempt.
The general expression of the nth term is a formula that can be used to find any term in a sequence or series, given its position in the sequence. It is typically denoted as an or un.
To find the general expression of the nth term, you must first identify the pattern in the given sequence or series. This can be done by looking at the differences between consecutive terms or by using other mathematical techniques. Once the pattern is identified, you can write a formula to represent it, using n as the variable for the position of the term.
Finding the general expression of the nth term allows us to easily find any term in a sequence or series without having to list out all the previous terms. This is particularly useful when dealing with large or infinite sequences, as it saves time and effort. It also helps us to better understand the underlying pattern or rule governing the sequence.
Yes, the general expression of the nth term can be used for any type of sequence or series, as long as there is a consistent pattern or rule governing the terms.
Some common mistakes when finding the general expression of the nth term include assuming incorrect patterns, forgetting to include the variable n in the formula, and not checking the formula for accuracy by plugging in different values of n. It is important to carefully analyze the sequence and double-check the formula to ensure that it accurately represents the pattern.