Answer :

Here first term a = 63 and common difference d = 60 – 63 = -3.
Also, Sn = 693
Since the sum of n terms is
Sn =


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



693 × 2 = n[ 126 + (n - 1)(-3)]
1386 = 126n - 3n(n - 1)
1386 = 126n - 3n2 + 3n
1386 = -3n2 + 129n
3n2 - 129n + 1386 = 0
n2 - 43n + 462 = 0
n = 21, n = 22
n = 21 or n = 22


Hence, Either 21 or 22 terms of the arithmetic progression must be taken to get sum as 693.


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