Question

The speed of a car decreases by 2 kmph after every one hour. If the distance travelled in the first one
hour was 63 km. What was the total distance travelled by the car in 9 hours

Answer 1

According to the Question, Speed of the decreases after every 1 hours.
Thus, In the total time of 9 hours, speed of the car will be decreased 9 times.

The sequence of the speed of the car in the total time of 9 hours will be in A.P. since each term will be differs by the Preceding term by -2. 

Therefore, 
 Common difference (d) = -2
First term (or speed in the first hours) = a
= 63/1
= 63 km/hr.

Number of terms(n) = 9 hrs.

tₐ = a + (n-1)d
∴ t₉ = a + (9-1)-2
   = (63 - 16)
   = 47 


Now, Using the Formula,
Sn = n/2 (a + l)
where, l is the last term or you can say that (a - 16).

∴ Sn = 9/2[63 + 47]
  Sn = 4.5[110]
 Sn = 495 


Hence, the total distance traveled by the car in 9 hours is 495 km.


Hope it helps.

Answer 2

Given :

The distance travelled in first
one hour is 63 km

2 km of distance decreases for every
one hour of travel

The distance travelled in next one hour is
61 km and so on.

It forms the following AP.

63, 61, 59 ............

Here a= 63 and d = -2


The total distance travelled in 9 hours

= sum of the travelled in every hour up to
9 hours

i.e
S(n) = n/2 [2a + (n-1)d]

S(9)
= 9/2 [2×63 + 8(-2)]

= 9/2 [ 126 -16]

= 9/2 × 110

= 9 × 55

= 495 kms