Ex 5.3, 16 - Chapter 5 Class 10 Arithmetic Progressions

Transcript

Ex 5.3 ,16 A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes. Let the 1st prize be a So the 2nd prize = a 20 The 3rd prize = (a 20) 20 = a 40 And so on So, the series will be a, a 20, a 40, . Since difference is same, it is an AP Here, sum of Rs 700 is given, So, Sn = 700 Also, a = a d = (a 20) a = a 20 a = 20 We know that Sn = /2 (2 +( 1) ) Putting the values Sn = /2 (2a + (n 1) d) 700 = 7/2 (2 +(7 1) 20) 700 = 7/2 (2 +6 20) 700 = 7/2 (2 120) 700 2/7=2 120 200 = 2a 120 200 + 120 = 2a 320 = 2a 320/2= 160 = a a = 160 So, 1st prize = a = 160 2nd prize = a 20 3rd prize = a 40 4th prize = a 60 5th prize = a 80 6th prize = a 100 7th prize = a 120