Write an expression for the nth term of the sequence. (There is more than one correct answer.) 1,...
Question:
Write an expression for the {eq}n {/eq}th term of the sequence. (There is more than one correct answer.)
{eq}\displaystyle 1,\ 7,\ 13,\ 19,\ .\ .\ . {/eq}
Arithmetic sequence:
A sequence of form {eq}a, \ a+d, \ a+2d,... {/eq} is called the arithmetic sequence where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference. The {eq}n {/eq}th term of the sequence is given by the formula {eq}a_n=a+(n-1)d {/eq} where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference.
Answer and Explanation: 1
We have the sequence {eq}\displaystyle 1,\ 7,\ 13,\ 19,\ .\ .\ . {/eq}
Here,
First term=1
Second term=7
Third term=13
Consider the difference,
Second term -First term=7-1=6
and Third term -Second term=13-7=6
Thus the given sequence is an arithmetic sequence.
The {eq}n {/eq}th term of the sequence is given by the formula {eq}a_n=a+(n-1)d {/eq} where {eq}a {/eq} is the first term, {eq}d {/eq} is a common difference.
We have {eq}a=1, \ d=6 {/eq}
Therefore the {eq}n {/eq}th term of the given sequence is {eq}1+(n-1)6 \\ =1+6n-6 \\ =6n-5 {/eq}
This is the required {eq}n {/eq}th term.
Learn more about this topic:
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Chapter 25 / Lesson 1Geometry studies the properties of shapes, solids, points, lines, and surfaces. To understand geometry, students need geometric thinking. Learn about the progression of geometric thinking, including visual, descriptive, analytic, and abstract stages.