The speed of the bus increases by 2 kmph after every one hour . If the distance travelled in the first one hour was 20 km , what was the total distance travelled in 12 hours ?

Step 1: Understand the problem The problem states that a bus increases its speed by 2 km/h every hour. In the first hour, it travels 20 km. We need to find the total distance it travels in 12 hours.

Step 2: Identify the pattern The bus starts at 20 km/h and increases its speed by 2 km/h every hour. This means that the speed of the bus each hour forms an arithmetic sequence: 20, 22, 24, 26, ..., up to the 12th hour.

Step 3: Find the speed in the 12th hour The nth term of an arithmetic sequence can be found using the formula: a + (n - 1)d, where a is the first term, d is the common difference, and n is the term number. In this case, a = 20 km/h, d = 2 km/h, and n = 12. Substituting these values into the formula gives: 20 + (12 - 1)2 = 42 km/h.

Step 4: Find the total distance The total distance travelled by the bus in 12 hours is the sum of an arithmetic series. The sum, S, of the first n terms of an arithmetic series can be found using the formula: S = n/2 * (a + l), where a is the first term, l is the last term, and n is the number of terms. In this case, a = 20 km, l = 42 km, and n = 12. Substituting these values into the formula gives: S = 12/2 * (20 + 42) = 6 * 62 = 372 km.

So, the total distance travelled by the bus in 12 hours is 372 km.