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 progression 20, 60, 100, 140, …. Find the distance that the projectile traveled in the 9th second.

Answer 1

This is an arithmetic progression which means it either decreases or increases at a constant rate. We know the first few terms here, that is: 20, 60, 100, 140..

In an arithmetic progression terms are sort of like this: a, a + d, a + 2d, a + 3d...
Where a is the first term, d is the common difference. This means that in our sequence, a = 20 and a + d = 60. So we know what a is, we have to find what d is. We know that a + d = 60 and a = 20. If we subtract the two as in (a + d) - (a), we can solve for d. So:

(a + d) - (a) = d = 60 - 20 = 40 --> So our d = 40.

Now we know that the progression is a, a + d, a + 2d, a + 3d, a + 4d, a + 5d...Any term in an arithmetic progression is given by: t = a + (n-1)d, where d is once again the common difference, a is the first term, and n is the term number.

We are asked to find the 9th term, so n = 9. We know that a = 20 and d = 40. So we plug this in to the formula:

t = a + (n - 1)d
t = 20 + (9 - 1)40
t = 20 + (8)40
t = 20 + 320
t = 340

Therefore, the 9th term in the arithmetic progression is 340.

@selenamalter