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.
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Let the First prize be a then, Second prize = a – 20 third prize = (a – 20) – 20 = a – 40 And so on hence the sequence will be a, a – 20, a – 40,….
Here, a = a d= (a – 20) – a = a – 20 – a = -20 ∴ the given sequence is an A.P. Also, Sum of Rs 700 is given, So, Sn = 700 We know that
So, First prize = a = Rs 160 Second prize = a – 20 = 160 – 10 = Rs 140 Third prize = a – 40 = 160 – 40 = Rs 120 Furth prize = a – 60 = 160 – 60 = Rs 100 Fifth prize = a – 80 = 160 – 80 = Rs 80 Sixth prize = a – 100 = 160 – 100 = Rs 60 Seventh prize = a – 120 = 160 – 120 = Rs 40