Question

how many terms of AP 63, 60,57.... taken
so that their sum is 693

Answer 1

Hey dear friend

Given A.P.= 63,60,57.,.,.,.
Sn=693

a=63 d=60-63= -3 Sn=693

By formula=>Sn=n/2[2a+(n-1)d]
Substituting all values

693=n/2[2*63+(n-1)(-3)]
693=n/2[126-3n+3]
693*2=n[129-3n]
1386= -3n²+129n
1386/3= -3n²/3+129n/3
462= -n²+43n

n²-43n+462=0
By mid term splitting

n²-21n-22n+462=0
n{n-21)-22(n-21)=0
(n-21)(n-22)=0

n-21=0
n=21

n-22=0
n=22

So, the no. of terms can be 21 and 22.

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