Question

During the first second of a journey, a car travels 2m. it travels 4m during the second, 6m during the third, second and so on .

Assuming that the distance continue to 11X rease in a linear sequence find
(a) the distance travelled in the tenth seconds
(b) total distance travelled up to the tenth seconds

Answer 1

The distance traveled in the tenth second is 20 meters, and the total distance traveled up to the tenth second is 110 meters. This is determined by using the formula for the nth term of an arithmetic sequence and the formula for the sum of the first n terms of an arithmetic sequence.

Step-by-step explanation:

The question presents a scenario where a car is traveling different distances in each consecutive second, increasing by a linear sequence. To solve this problem, first, we have to determine the distance traveled in the tenth second. The distance covered each second forms an arithmetic sequence. The formula for the nth term in an arithmetic sequence is given by:

an = a1 + (n - 1) * d

Where an is the nth term, a1 is the first term, d is the common difference, and n is the term number

Part (a): To find the distance traveled in the tenth second:

a10 = 2 m + (10 - 1) * 2 m = 2 m + 18 m = 20 m

The distance traveled in the tenth second is 20 meters.

Part (b): The total distance traveled up to the tenth second can be found by summing the arithmetic sequence, using the formula for the sum of the first n terms of an arithmetic sequence:

Sn = n/2 * (2a1 + (n - 1) * d)

S10 = 10/2 * (2 * 2 m + (10 - 1) * 2 m) = 5 * (4 m + 18 m) = 5 * 22 m = 110 m

The total distance traveled up to the tenth second is 110 meters.