NDA Maths Mock Test – 01 – Q10

If p^th, q^th and r^th terms of an A.P. are in G.P., then the common ratio of this G.P. is

• pqr
• pq
• (p – q)/(q – r)
• (q – r)/(p – q)

As per the question,
i Let a be the first term and d be the common difference of the gi√en A.P.
‘ Then, we write,
pth term, ap=a+ (p- 1)d
qth term, aq =a + (q- 1)d
‘ rth term, ar=a + (r- 1)d ‘
Now, according to the question the path, the qth and the rth terms are in G.P.
bP)
S@t@-DdT=@+t@pE-1)dx@t+-1)d
! = a?+2aq- d+ (q- D2 =a +ad(r-1+p-1)+(p- 1) r-1)d> !
ggg yg Lg SE SE pp
‘ = ad2q-2-r-p+2)+d3(q*-2q+ L-pr+p+r-1)=0
= a(2q-r-p)+d(g?-2q-pr+p+1)=0(.d cannot be 0)
@
_ (q —2q—pr+p+r)d
‘ =a (2q—r-p)
+.» Common ratio, r = 2 1
»
‘ ated
H ~ at(p-1)d
H (a2-20-pripir)a H
1 _ Tag ted
1 2 2g-priptr)d
—- = J +Hp-1)d
_ @’-2q-pripiripgirg-2¢°—p-r+2q
q2>—2q—pr+p+r+p*+pr—2pg—p—r+2q
_ pa—pr—a*+ar
Pa’ —2pq
_ plg=r)—ala=r)
! a” !
‘ _ (alan)
H (a)
_ (g=7)
1 (p—9)
NU
1 ®) 3
‘