Find the nth term of the sequence: {eq}1, \frac{8}{7}, \frac{5}{4}, \frac{4}{3} {/eq},... Assume obvious pattern continues.

## Question:

Find the nth term of the sequence: {eq}1, \frac{8}{7}, \frac{5}{4}, \frac{4}{3} {/eq},... Assume obvious pattern continues.

## Data Points; Interpolation Polynomials:

Given a set of {eq}n {/eq} data points {eq}(x_i, y_i) {/eq} for non-equal {eq}x_i {/eq}'s, a polynomial

{eq}{\displaystyle p:\mathbb {R} \rightarrow \mathbb {R} } {/eq} is said to interpolate the data if {eq}p ( x_j ) = y_j {/eq} for each {eq}{\displaystyle j\in \{1,\dotsc ,n\}} {/eq}.

We'll use a polynomial of degree {eq}3 {/eq} to interpolate the points in the sequence given in the problem statement.

## Answer and Explanation: 1

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View this answerThe data in the sequence can be continued in infinitely many non-trivial form. Not having noticed a simple pattern, which might exist, we'll consider...

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Chapter 12 / Lesson 1Learn about the definition of sequence in math. Understand what finite and infinite mathematical sequences are and how they are represented. See examples of famous mathematical sequences that are commonly used.