Question

A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles.
The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 17, 51, 85, 119, ... Find the total distance that the projectile traveled in the ninth second.

Answer 1

Since the sequence starts at 17 and goes to 51 you want to find out how the numbers are become larger. if you take 51 and subtract 17 it equals 34 and you do the same with 85 and 51 and you still get 34 so every second the asteroid travels 34 ft per second. then to find out when it is at the 9th second 17 was the first second so 51 was the second and 85 was the third and 119 was the 4th so you add 34 to 119 5 times to get the 9th second which would be 289 ft. well please give me the brainliest.

Answer 2

Answer:

Total distance traveled in ninth second is:

289 feet.

Step-by-step explanation:

The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence :

17, 51, 85, 119, ...

i.e. we have:

$a_1=17\ , a_2=51\ ,a_3=85\ ,a_4=119\ ,........$

Since, $a_2=a_1+d$

where d represents the common difference of the sequence.

$51=17+d\\\\d=51-17\\\\d=34$

Hence, the ninth term of the sequence is the total distance that the projectile traveled in the ninth second i.e.

$a_9=a_1+8d\\\\a_9=17+8\times 34\\\\a_9=289$

Hence, the total distance traveled in the ninth second is:

289 feet.