# Find the first four terms of the sequence with a recursive formula. \displaystyle u_1=3, \; u_n =...

## Question:

Find the first four terms of the sequence with a recursive formula.

{eq}\displaystyle u_1=3, \; u_n = 2 \times u_{n-1}-1,\; n \geq 2 {/eq}

## Recursive formula:

One way to define a numerical sequence is through a recursive formula.

A recursive formula, relates the general term of a sequence to the elements before or after of the sequence.

## Answer and Explanation: 1

Considering the sequence given by the recursive formula {eq}\displaystyle u_1=3, \; u_n = 2 \times u_{n-1}-1,\; n \geq 2 {/eq}, using this expression and substituting the values of the index {eq}n {/eq} by the numbers, {eq}2,\;3 {/eq} and {eq}4 {/eq}, we can determine the other first three terms of the sequence:

{eq}\displaystyle { n = 2 \to {u_2} = 2{u_1} - 1\\ {u_1} = 3\\ {u_2} = 2 \cdot 3 - 1\\ {u_2} = \boxed{5}\\ \\ n = 3 \to {u_3} = 2{u_2} - 1\\ {u_3} = 5\\ {u_3} = 2 \cdot 5 - 1\\ {u_3} = \boxed{9}.\\ \\ n = 4 \to {u_4} = 2{u_3} - 1\\ {u_4} = 9\\ {u_4} = 2 \cdot 9 - 1\\ {u_4} = \boxed{17}. } {/eq}

So, the first four terms of the sequence are the values: {eq}\displaystyle {u_1} = 3,\;{u_2} = 5,\;{u_3} = 9,\;{u_4} = 17. {/eq}

#### Learn more about this topic:

from

Chapter 21 / Lesson 12Find out what a recursive rule is. Learn how to write a recursive rule. See an examples of a geometric recursive formula and an arithmetic recursive formula.