Question

find the number of terms in the finite arithmetic sequence.\\{9,16,23,\ldots,107\\}\
select one:\
\bigcirc a. 107\
\bigcirc b. 98\
\bigcirc c. 15\
\bigcirc d. 7

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 number of terms.

Step2: Identify known values

$a_1 = 9$, $a_n = 107$, $d = 16 - 9 = 7$

Step3: Substitute values into formula

$107 = 9 + (n-1) \times 7$

Step4: Solve for n

First, subtract 9 from both sides:
$107 - 9 = (n-1) \times 7$
$98 = (n-1) \times 7$
Then divide both sides by 7:
$\frac{98}{7} = n-1$
$14 = n-1$
Finally, add 1 to both sides:
$n = 14 + 1 = 15$

Answer:

C. 15