Find the 44th term of this arithmetic sequence.
[tex]$\begin{array}{c}
2,7,12,17,22, \ldots \
a_{44}=[?]\end{array}$[/tex]
Hint: [tex]$a_n=a_1+(n-1) d$[/tex]
Answer (2)
Identify the first term a 1 = 2 and the common difference d = 5 .
Use the formula for the nth term of an arithmetic sequence: a n = a 1 + ( n − 1 ) d .
Substitute n = 44 , a 1 = 2 , and d = 5 into the formula: a 44 = 2 + ( 44 − 1 ) 5 .
Calculate the 44th term: a 44 = 217 . The final answer is 217 .
Explanation
Identifying the Given Information We are given an arithmetic sequence and asked to find the 44th term. The sequence is 2, 7, 12, 17, 22, ... We can see that the first term, a 1 , is 2 and the common difference, d , is 7 − 2 = 5 . We are also given the formula for the nth term of an arithmetic sequence: a n = a 1 + ( n − 1 ) d .
Applying the Formula We want to find the 44th term, so n = 44 . We have a 1 = 2 and d = 5 . Substituting these values into the formula, we get: a 44 = a 1 + ( 44 − 1 ) d = 2 + ( 43 ) ( 5 )
Calculating the 44th Term Now we calculate the value: a 44 = 2 + ( 43 ) ( 5 ) = 2 + 215 = 217 So, the 44th term of the arithmetic sequence is 217.
Examples
Arithmetic sequences are useful in many real-life situations. For example, if you save a fixed amount of money each month, the total amount you've saved over time forms an arithmetic sequence. Understanding arithmetic sequences helps you predict future savings or plan for regular expenses. Another example is calculating the number of seats in a stadium where each row has a fixed number of additional seats compared to the previous row. These sequences can also model simple growth patterns or depreciation.
The 44th term of the given arithmetic sequence is calculated using the formula for the nth term. After identifying the first term as 2 and the common difference as 5, applying the formula gives us a final answer of 217. Therefore, a 44 = 217 .
;
