Let the first three terms 2, p and q , with q 2 , of a G.P. be respectively the 7^ th , 8^ th and 13^ th terms of an A.P. If the 5^ th term of the G.P. is the n^ th term of the A.P., then n is equal to:

Step-by-step solution

p^2=2 q2=a+6 d ...(i) p = a +7 ~d ...(ii) q=a+12 d ...(iii) p -2= d ((ii) - (i)) q-p=5 d ((iii) - (ii)) q-p=5 d aligned & q-p=5(p-2) & q=6 p-10 & p^2=2(6 p-10) & p^2-12 p+20=0 & p=10,2 & p=10 ; q=50 & d=8 & a=-46 & 2,10,50,250,1250 & a^4=a+(n-1) d & 1250=-46+(n-1) 8 & n=163 aligned