Answer of Comment – asked in YouTube channel

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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Ans.

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

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