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yakin said:Ok i got that, then they have simplified that expression to this expression how did they get this
\(\displaystyle (2 + 2c)n + ( 2d – 3c) = 0\)
yakin said:I got it sir. Thanks!
Ok Mark.MarkFL said:We're pretty laid back and informal here...you can just call me Mark if you like. (Handshake)
The equation represents a recursive sequence, where each term is determined by the previous term and the value of n. The first part, "a_n=3a_n-1 + 2n", calculates the value of a specific term, while the second part, "cn + d = 3(c(n-1) + d) + 2n", generalizes the formula for any term in the sequence.
This equation is often used in mathematical modeling and data analysis. It can help predict the behavior of a system or process over time, and can also be used to generate numerical solutions to various problems in physics, biology, and other scientific fields.
The variables in this equation are a_n, c, d, and n. a_n represents the value of a specific term in the sequence, while c and d are constants that determine the general formula for any term. n represents the position of the term in the sequence.
This equation can be solved using various methods, such as substitution or iteration. By plugging in different values of n, the formula can be applied to find the value of the desired term. Additionally, the equation can be rearranged to solve for a specific variable, such as finding the value of n when a_n is known.
This equation can be applied to many real-world situations, such as population growth and compound interest. It can also be used to model physical processes, such as the motion of objects under the influence of gravity. In computer science, this equation can be used to generate sequences for algorithms and data structures.