A sequence is defined by the rule
[tex]$x_n=8 n-17$[/tex]
Work out the value of [tex]$x_6$[/tex].
Answer (1)
Substitute n = 6 into the expression for x n .
Calculate x 6 = 8 ( 6 ) − 17 .
Simplify the expression to find x 6 = 48 − 17 .
The value of x 6 is 31 .
Explanation
Understanding the Problem We are given the sequence defined by the rule x n = 8 n − 17 , and we want to find the value of x 6 . This means we need to substitute n = 6 into the formula for x n .
Substituting n=6 To find x 6 , we substitute n = 6 into the expression x n = 8 n − 17 :
x 6 = 8 ( 6 ) − 17
Calculating x_6 Now, we perform the calculation: x 6 = 48 − 17 = 31
Final Answer Therefore, the value of x 6 is 31.
Examples
Sequences are used to model various real-world phenomena, such as population growth, compound interest, and the motion of objects. For example, if you save a fixed amount of money each month, the total amount you have saved over time forms a sequence. Understanding sequences helps in predicting future values and making informed decisions.
