Question

if the first term of an arithmetic sequence is 50 and the sixth term is 90, what is the 10th term? select one: a. 122 b. 130 c. 290 d. 302

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, $n$ is the term number, and $d$ is the common difference.

Step2: Plug in 6th term values

We know $a_1=50$, $a_6=90$, $n=6$. Substitute into the formula:
$90 = 50 + (6-1)d$

Step3: Solve for common difference $d$

Simplify and solve for $d$:
$90 - 50 = 5d$
$40 = 5d$
$d = \frac{40}{5} = 8$

Step4: Calculate the 10th term

Use $a_1=50$, $n=10$, $d=8$ in the formula:
$a_{10} = 50 + (10-1)\times8$
$a_{10} = 50 + 72$

Answer:

B. 130