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. (1 point)
Responses
534 feet
560 feet
212 feet
426 feet
The common difference between each term is 18 (44-26 = 18, 62-44 = 18, 80-62 = 18).
To find the seventh term, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n-1)d, where a_1 is the first term, n is the term number, and d is the common difference.
a_7 = 26 + (7-1)18
a_7 = 26 + 6*18
a_7 = 26 + 108
a_7 = 134
The total distance traveled in seven seconds is the sum of the arithmetic sequence from 26 to 134. We can calculate this using the formula for the sum of an arithmetic series: S = (n/2)(a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term.
Plugging in the values:
S = (7/2)(26 + 134)
S = (7/2)(160)
S = 7*80
S = 560 feet
The total distance that the projectile traveled in seven seconds is 560 feet.
Therefore, the answer is 560 feet.