To find the value of [tex]\( x_{10} \)[/tex] in the sequence defined by the formula [tex]\( x_n = 7n + 13 \)[/tex], follow these steps:
1. Identify the term of the sequence that you need to compute. In this case, it is [tex]\( x_{10} \)[/tex], which signifies that [tex]\( n = 10 \)[/tex].
2. Substitute [tex]\( n = 10 \)[/tex] into the given formula [tex]\( x_n = 7n + 13 \)[/tex].
So, we have:
[tex]\[
x_{10} = 7(10) + 13
\][/tex]
3. Simplify the expression by performing the multiplication first:
[tex]\[
7 \times 10 = 70
\][/tex]
4. Now add the constant term 13 to the result of the multiplication:
[tex]\[
70 + 13 = 83
\][/tex]
Thus, the value of [tex]\( x_{10} \)[/tex] is [tex]\( 83 \)[/tex].
