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 progression 19, 57, 95, 133,... Find the distance that the projectile traveled in the seventh second.
a. 247 ft
b. 266 ft
c. 209 ft
d. 285 ft
just use what you know about APs
Clearly,
a = 19
d = 38
So a7 = 19+6*38 = ____
To find the distance that the projectile traveled in the seventh second, we need to determine the common difference (d) of the arithmetic progression and then calculate the seventh term (a₇).
The arithmetic progression is given by: 19, 57, 95, 133,...
To find the common difference (d), we subtract the second term from the first term:
d = 57 - 19 = 38
Now, we can calculate the seventh term using the formula for the nth term of an arithmetic progression:
a₇ = a + (n - 1)d
Substituting the values we have:
a₇ = 19 + (7 - 1)38
= 19 + 6 * 38
= 19 + 228
= 247
Therefore, the distance that the projectile traveled in the seventh second is 247 feet.
To find the distance that the projectile traveled in the seventh second, we need to determine the pattern or rule that governs the arithmetic progression given.
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is always the same. In this case, we need to figure out the common difference.
To find the common difference, we can subtract the first term from the second term:
57 - 19 = 38
Now that we have the common difference, we can find the distance traveled in the seventh second by adding six times the common difference to the first term:
Distance in the seventh second = 19 + (6 * common difference)
Since the common difference is 38, we substitute this value into the formula:
Distance in the seventh second = 19 + (6 * 38)
Calculation:
Distance in the seventh second = 19 + (6 * 38)
= 19 + 228
= 247
Therefore, the distance that the projectile traveled in the seventh second is 247 feet.