Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Answer 1

Answer: 69.75 miles

Step-by-step explanation:

The explicit rule for an arithmetic sequence is: $a_n=a_1+d(n-1)\ \text{where}\ a_1\ \text{is the first term and d is the difference}$

In the given problem, $a_1=1.75$ and d = 0.25

$a_n=1.75+0.25(n-1)\\.\quad=1.75+0.25n-0.25\\.\quad=0.25n+1.50\\\\a_{18}=0.25(18)+1.50\\.\quad=4.50+1.50\\.\quad=6.00$

The sum of an arithmetic sequence is: $S_n=\dfrac{a_1+a_n}{2}\cdot n$

$S_{18}=\dfrac{1.75+6}{2}\cdot 18\\\\.\quad=7.75\cdot 9\\\\.\quad=69.75$

Answer 2

Akim ran 69.75 miles in the course of 18 days.