The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?

The speed of a bus increases by 2 km after every one hour. If the dist

1.	The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?
Answer» Given that distance travelled in 1st hour = 35 km and speed of the bus increases by 2 km after every one hour Hence distance travelled in 2nd hour = 37 km Hence distance travelled in 3rd hour = 39 km .. Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)] This is an Arithmetic Progression(AP) with first TERM, a=35, number of terms,n = 12 and common difference, d=2. The sequence a , (a + d), (a + 2D), (a + 3D), (a + 4D), . . . is called an Arithmetic Progression(AP) where a is the first term and d is the common difference of the AP Sum of the first n terms of an Arithmetic Progression(AP), Sn = n/2[2a+(n−1)d] where n = number of terms Hence, [35+37+39+... (12 terms)] = S12 = 122[2 × 35 +(12 − 1)2] = 6[70 + 22] = 6 × 92 = 552 Hence the total distance travelled = 552 km