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Ex 5.3, 16 - Chapter 5 Class 10 Arithmetic Progressions
Last updated at May 29, 2023 by Teachoo
Ex 5.3
Ex 5.3, 1 (i)
Ex 5.3, 1 (ii)
Ex 5.3, 1 (iii) Important
Ex 5.3, 1 (iv)
Ex 5.3, 2 (i)
Ex 5.3, 2 (ii)
Ex 5.3, 2 (iii) Important
Ex 5.3, 3 (i)
Ex 5.3, 3 (ii)
Ex 5.3, 3 (iii)
Ex 5.3, 3 (iv) Important
Ex 5.3, 3 (v)
Ex 5.3, 3 (vi) Important
Ex 5.3, 3 (vii)
Ex 5.3, 3 (viii) Important
Ex 5.3, 3 (ix)
Ex 5.3, 3 (x)
Ex 5.3, 4
Ex 5.3, 5
Ex 5.3, 6 Important
Ex 5.3, 7
Ex 5.3, 8
Ex 5.3, 9
Ex 5.3, 10 (i)
Ex 5.3, 10 (ii) Important
Ex 5.3, 11 Important
Ex 5.3, 12
Ex 5.3, 13
Ex 5.3, 14 Important
Ex 5.3, 15
Ex 5.3, 16 Important You are here
Ex 5.3, 17
Ex 5.3, 18 Important
Ex 5.3, 19 Important
Ex 5.3, 20 Important
Chapter 5 Class 10 Arithmetic Progressions
Serial order wise
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, 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, a = a d = (a – 20) – a = a – 20 – a = –20 Also, Sum of Rs 700 is given, So, Sn = 700 We know that Sn = 𝒏/𝟐 (𝟐𝒂+(𝒏−𝟏)𝒅) Putting a = a, d = −20, Sn = 700 700 = 7/2 (2𝑎+(7−1)×−20) 700 = 7/2 (2𝑎+6 × −20) 700 = 7/2 (2𝑎−120) 700 × 2/7=2𝑎−120 200 = 2a – 120 200 + 120 = 2a 320 = 2a 320/2=𝑎 160 = a a = 160 So, 1st prize = a = Rs 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
