A large asteroid crashed into a moon of a 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 26, 44, 62, 80, . . . . Find the total distance that the projectile traveled in seven seconds.
To find the total distance the projectile traveled in seven seconds, we need to find the seventh term of the arithmetic sequence.
We can find the common difference by subtracting the first term from the second term:
44 - 26 = 18
Now we can find the seventh term:
a7 = 26 + (7-1) * 18
a7 = 26 + 6 * 18
a7 = 26 + 108
a7 = 134
Now, we can find the total distance the projectile traveled in seven seconds by summing the terms of the arithmetic sequence:
Total distance = 7/2 * (first term + last term)
Total distance = 7/2 * (26 + 134)
Total distance = 7/2 * 160
Total distance = 560 feet
Therefore, the total distance that the projectile traveled in seven seconds is 560 feet.