Question

At the 1998 Winter X-Games held in Crested Butte, Colorado, Jennie Waara, from Sweden, won the women’s snowboarding slope-style competition. Suppose that in one of the qualifying races, Ms. Waara traveled 5 feet in the first second, and the distance she traveled increased by 7 feet each subsequent second.
If Ms. Waara reached the finish line in 15 seconds, how far did she travel?

a.
646 feet
b.
790 feet
c.
766 feet
d.
810 feet


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

Answer:

Correct choice is D

Step-by-step explanation:

First second - 5 feet,

second second 5+7=12 feet,

third second  12+7=19 feet, i.e.

This rule represents the arithmetic sequence, where

$a_1=5,\\ \\d=7.$

You actually have to find $a_{15}$ that can be calculated using formula:

$a_n=a_1+(n-1)d.$

In your case,

$a_{15}=5+(15-1)\cdot 7=5+14\cdot 7=5+98=103\ ft.$

Then the sum of first 15 terms of the arithmetic sequence is the distance Ms. Waara traveled.

The sum of n terms of the arithmetic sequence is

$S_n=\dfrac{a_1+a_n}{2}\cdot n,$

that in your case takes look

$S_{15}=\dfrac{5+103}{2}\cdot 15=810\ ft.$