Question

find the number of terms in the finite arithmetic sequence. {4,9,14,…,99} select one: a. 99 b. 20 c. 5 d. 95

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

$a_1 = 4$, $a_n = 99$, $d = 9 - 4 = 5$

Step3: Substitute values into formula

$99 = 4 + (n-1) \times 5$

Step4: Solve for n

First, subtract 4 from both sides:
$99 - 4 = (n-1) \times 5$
$95 = (n-1) \times 5$
Then divide both sides by 5:
$\frac{95}{5} = n - 1$
$19 = n - 1$
Finally, add 1 to both sides:
$n = 19 + 1 = 20$

Answer:

B. 20