The 20th term of the sequence √(5), √(20), √(45), ……is (a) 20 √(3) (b) 20 √(5) (c) 10 √(5) (d) 1

step 1 In this problem, first I am writing the sequence under root 5, root 20, root 45, dot, dot, dot,

The 20th term of the sequence √(5), √(20), √(45), ……is (a)...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Radical Expression Simplification

This concept focuses on simplifying expressions involving square roots by factoring out perfect squares. Recognizing and extracting these allows one to rewrite the terms in a more manageable form, which is key in matching them to a given pattern.

General Term Formulation

Once a pattern is recognized, formulating the general term (nth term) is essential. This converts the observed pattern into an algebraic expression that can calculate any term in the sequence, such as expressing the term as a product of its index and a constant factor after simplification.

Sequences and Series

This concept involves understanding ordered lists of numbers defined by a specific rule. In such sequences, each term is generated by applying a function or formula based on its position in the list, and recognizing the pattern allows the determination of any term in the sequence.

Pattern Recognition in Sequences

This involves identifying consistent trends or structures within a series of numbers. By analyzing the given sequence, one can detect that the numbers under the square roots are multiples of a constant factor times perfect squares, which leads to a general rule for generating subsequent terms.

Please give Ace some feedback