Question

the distance traveled by a swinging pendulum decreases after each swing. The first wings distance was 625 mm, The second was 500 mm the third, 400. What was the swing distance be for the seventh swing?

Answer 1

The distance for the seventh swing of the pendulum is approximately 163.84 mm.

Step-by-step explanation:

The distance traveled by a swinging pendulum decreases after each swing. To find the distance for the seventh swing, we can observe that the distances form a pattern. The first swing distance is 625 mm, the second swing distance is 500 mm, and the third swing distance is 400 mm. We can see that each subsequent swing distance is obtained by multiplying the previous swing distance by a factor of 0.8. So, to find the distance for the seventh swing, we can use the formula:

Distance = 625 mm * (0.8)⁶

Calculating this, we get:

Distance = 625 mm * 0.262144 = 163.84 mm

Therefore, the distance for the seventh swing would be approximately 163.84 mm.

Answer 2

163.84 mm

Step-by-step explanation:

The swing distances form a geometric sequence with first term 625 and common ratio 500/625 = 0.8. The formula for the general term of such a sequence is ...

an = a1×r^(n-1)

Then the 7th term of the sequence will be ...

a7 = 625×0.8^(7-1) ≈ 163.84 . . . mm