1Sn=a,
S2n-Sn=b, so S2n=a-b;
S3n-S2n=c ;
solving, an applying GP summation formula
x(1-rn)/(1-r)=a
b=xrn(1-rn)/(1-r)
c=xr2n(1-rn)/(1-r)
Ques1) Let a,b,c are respectively the sum of the first n terms, the next n terms, and the next n terms of a G.P. Show that a,b,c are in G.P.
Ques2) Show that the sum of square of three consecutive odd no's increase by 1 is divisible by 12 but not by 24.
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112) According to qsn, the sum turns out to be M= (2a-3)2+(2a-1)2+(2a+1)2+1=12(a2-a+1)... Now separately take cases where a is evn or odd, and each case it turns out to be of the form 24k+12, thus 12|M, but 24 does not....
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