Question

mom: ch. 6 review
score: 29.61/33 answered: 30/33
question 19
which term of the arithmetic sequence 1, 7, 13, 19, ... is 253?
it is the □ th term.
question help: video

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

From the sequence: $a_1 = 1$, $d = 7-1 = 6$, $a_n = 253$

Step3: Substitute values into formula

$253 = 1 + (n-1) \times 6$

Step4: Simplify and solve for n

First, subtract 1 from both sides:
$253 - 1 = (n-1) \times 6$
$252 = (n-1) \times 6$
Then divide both sides by 6:
$\frac{252}{6} = n-1$
$42 = n-1$
Finally, add 1 to both sides:
$n = 42 + 1 = 43$

Answer:

43