# Given that the nth term of a sequence is given by the formula 4n+5, what are the first three...

## Question:

Given that the nth term of a sequence is given by the formula 4n+5, what are the first three terms of the sequence?

## Using the general formula to find the nth term in a sequence:

A mathematical sequence is a series of numbers that have a common mathematical pattern. This pattern can then be observed by looking at the relationship of the previous and the succeeding term in a sequence. After a certain pattern is observed, it will then be converted into an algebraic expression which can be used to determine the succeeding terms in a sequence.

## Answer and Explanation: 1

We can start the sequence at {eq}n = 1 {/eq}. To determine the first three terms of the series, we will substitute {eq}n = 1, 2, 3 {/eq} on the nth term of the sequence. This yields

$$\begin{align} 4n + 3& = 4(1) + 3 &\left[\text{Substitution of values}\right]\\[0.2cm] & = 4 + 3\\[0.2cm] & = 7\\[0.2cm] \\[0.2cm] 4n + 3& = 4(2) + 3 &\left[\text{Substitution of values}\right]\\[0.2cm] & = 8 + 3\\[0.2cm] & = 11\\[0.2cm] \\[0.2cm] 4n + 3& = 4(3) + 3 &\left[\text{Substitution of values}\right]\\[0.2cm] & = 12 + 3\\[0.2cm] & = 15\\[0.2cm] \end{align} $$

The first three terms are {eq}7 {/eq}, {eq}11 {/eq}, and {eq}15 {/eq}

#### Learn more about this topic:

from

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.