Given:Initial speed of vehicle = 42 km/h Increment of speed every hour = 6 km/h Distance between the points A and B = 420 km Formula used: Sn = (
n
2
){2a + (n – 1)d} Sn = Sum of terms in arithmetic progression n = Number of terms a = First term d = Difference Calculation: Sn = 420 a = 42 d = 6 420 = (
n
2
){2 × 42 + (n – 1) × 6 ⇒ 840 = n{84 + 6n – 6} ⇒ 840 = n{78 + 6n} ⇒ 840 = 78n + 6(n)2 ⇒ 6n2 + 78n – 840 = 0 ⇒ n2 + 13n – 140 = 0 By factorizing we get, ⇒ n = 7 ∴ The time taken by the vehicle to complete the distance is 7 h.