Question
The sum of the first 163 terms of a GP is equal to the
sum of the first 161 terms in the same GP. If the 117th term in the same GP is 985, then what will be the sum of 150 terms?Solution
According to the question,  if we take a(r163-1)/ r-1 =a(r161-1)/r-1 r163 = r161 r2 =1  r=±1  r = +1, the sum will be undefined. Taking r = -1, T117 = ar117-1 985 = a (-1)116 a=985 S150 =a(1-r")/1-r       (r 985(1-(-1)150)/1+1 985(1-1)/2=0 =0
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