Question

question 13
which term of the arithmetic sequence 1, 3, 5, 7, ... is 83?
it is the ____ th term.
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Explanation:

Step1: Recall arithmetic sequence formula

The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.

Step2: Identify known values

For the sequence 1, 3, 5, 7, ...:
$a_1 = 1$, $d = 3-1 = 2$, $a_n = 83$

Step3: Substitute values into formula

$83 = 1 + (n-1) \times 2$

Step4: Solve for n

First, subtract 1 from both sides:
$83 - 1 = (n-1) \times 2$
$82 = 2(n-1)$
Then divide both sides by 2:
$\frac{82}{2} = n-1$
$41 = n-1$
Finally, add 1 to both sides:
$n = 41 + 1 = 42$

Answer:

42