Grade 11Algebra

If pth , qth, rth term of an AP are in GP , then common ratio of this GP is

(p-q)/(q-r)

(q-r)/(p-q)

pqr

none of this

Pratyush Ranjan Roul

9 Years agoGrade 11

2 Answers

moumi roy

9 Years ago

as this is in AP 2q=p+r----eq(1)

as in GP q=p.c & r=p*c² where c=common difference,

putting in eq(1) 2*p.c=p+p*c² hence c^2+1-2c=0 or ( c-1)²=0 so c=1

frm(1) p-q=q-r or (p-q)/(q-r)=1=c or(q-r)/(p-q)=1=c so both can be the answer

Tushar Avhad

8 Years ago

Given that. pth ,qth,rth. Terms of an ap are in gp..therefore a+(q-1)d. a+(r-1)d-------------------- = -----------------(since they are a+(p-1)d. a+(q-1)d. Are in gp)Now,Let a+(q-1)d. a+(r-1)d-------------------- = -----------------= k a+(p-1)d. a+ (q-1)dBy theorem on equal ratiosWe geta+ qd-d -(a+rd-d)----------------------------=ka+pd-d-(a+qd-d)On simplifying we get qd-rd------------------=k pd-qd d(q-r)----------=kd(p-q) Therefore (q-r)-------------=k (P-q)Hope this will help u