Write an expression for the nth term of the sequence 10,22,34,46,.... 1. 12n-2\\2. 24n+2\\3....
Question:
Write an expression for the nth term of the sequence {eq}10,22,34,46,.... {/eq}
{eq}1.) \ 12n-2 \\ 2.) \ 24n+2 \\ 3.) \ 10n+12 \\ 4.) \ 12n+2 \\ 5.) \ 14n-12 {/eq}
Arithmetic Sequence
An arithmetic sequence is a type of sequence in which the difference of a term and its preceding term is a constant. This constant value is known as the common difference in the sequence. Mathematically, it is denoted by {eq}\displaystyle a_{n}=a_{1}+\left ( n-1 \right )d {/eq} where {eq}\displaystyle a_{n} {/eq} represents the nth term, {MathJax fullWidth='false'
\displaystyle a_{1} }] is the first term, and {MathJax fullWidth='false'
\displaystyle d }] is the common difference.
Answer and Explanation: 1
1. Consider the given sequence.
$$10,22,34,46,......... $$
2. Identify the first term {eq}\displaystyle a_{1} {/eq} and the common difference {eq}\displaystyle d {/eq}.
$$a=10,\\ d=22-10=12 $$
Note that the common difference is constant no matter what two consecutive terms we choose.
3. Finally, write the general formula for the nth term of sequence by substituting the values of the first term {eq}\displaystyle a_{1} {/eq} and the common difference {eq}\displaystyle d {/eq}. Simplify the resulting formula.
$$\begin{align} a_{n}&=a+\left ( n-1 \right )d\\ &=10+\left ( n-1 \right )12\\ &=10+12n-12\\ &=12n-2 \end{align} $$
Hence, option (1) is correct the answer.
Learn more about this topic:
from
Chapter 21 / Lesson 4Learn the Arithmetic sequence formula and meaning. Discover how to find the common difference and read arithmetic sequence examples.