Question

Arithmetic and Geometric Sequences Grade 11

A toy car is rolling down an inclined track and picking up speed as it goes. The car travels 4 cm in the first second, 8cm in the second second, 12cm in the next second, and so on. Determine the total distance travelled by the car in 30 seconds.

Answer 1

The distance traveled by the car in each second is increasing by 4 cm each time. This is an example of an arithmetic sequence, where the common difference is 4 cm.

To find the total distance traveled by the car in 30 seconds, we can use the formula for the sum of an arithmetic series:

S_n = n/2 * (a_1 + a_n)

where S_n is the sum of the first n terms of the series, a_1 is the first term (4 cm in this case), a_n is the nth term, and n is the number of terms.

Substituting the values into the formula:

S_n = 30/2 * (4 + (4 + (30 - 1) * 4))

S_n = 30/2 * (4 + 4 + 116)

S_n = 30/2 * 124

S_n = 3720 cm

So the total distance travelled by the car in 30 seconds is 3720 cm.