Find the nth term of a sequence whose first several terms are given.
{eq}1, 5, 9, 13,... {/eq}
Question:
Find the nth term of a sequence whose first several terms are given.
{eq}1, 5, 9, 13,... {/eq}
Arithmetic Sequence:
An arithmetic sequence has a constant difference between successive terms.
If {eq}a{/eq} is the initial term and {eq}d{/eq} is the common difference then the nth term will be given by,
{eq}t_n=a+(n-1)d{/eq}
We can determine {eq}a{/eq} and {eq}d{/eq} for the given problem.
Then using the formula above we can find the nth term of given sequence.
Answer and Explanation: 1
Given sequence,
{eq}1, 5, 9, 13, ... {/eq}
First term of the sequence is {eq}a=1{/eq}
The difference between successive terms is constant and given by {eq}d=4{/eq}.
Hence given sequence is an arithmetic sequence with,
a=1, d=4
{eq}\begin{align} \text{nth term }&= a+(n-1)d \\ t_n &=1+(n-1)(4) \\ \color{blue}{t_n} & \color{blue}{=4n-3} \end{align} {/eq}
Learn more about this topic:
from
Chapter 26 / Lesson 3Discover the arithmetic sequence definition and how math uses it. Know its formula and how to solve problems relating to it through sample calculations.