A sequence is defined by the rule [tex]x_n=7 n+13[/tex]. Work out the value of [tex]x_{10}[/tex]. (Hint: [tex]x_{10}[/tex] is the [tex]10^{\text {th }}[/tex] term in the sequence.)
Answer (1)
Substitute n = 10 into the sequence formula: x 10 = 7 ( 10 ) + 13 .
Perform the multiplication: x 10 = 70 + 13 .
Add the numbers: x 10 = 83 .
The 10th term in the sequence is 83 .
Explanation
Understanding the Problem We are given a sequence defined by the rule x n = 7 n + 13 , and we want to find the value of the 10th term, x 10 . This means we need to substitute n = 10 into the given formula.
Substituting n = 10 Now, let's substitute n = 10 into the formula: x 10 = 7 ( 10 ) + 13
Performing Multiplication Next, we perform the multiplication: x 10 = 70 + 13
Adding the Numbers Finally, we add the two numbers: x 10 = 83
Final Answer Therefore, the value of the 10th term in the sequence is 83.
Examples
Imagine you're tracking the number of apples a tree produces each year. If the number of apples follows a sequence like x n = 7 n + 13 , where n is the year, you can predict how many apples the tree will produce in the 10th year by substituting n = 10 into the formula. This gives you x 10 = 7 ( 10 ) + 13 = 83 apples. Understanding sequences helps in predicting growth or decline in various real-life scenarios, from population growth to financial investments.
