If the pth term of an AP is q and its qth term is p then show that its (p+q)th term is zero.
Asked by ash.au94
| 24th Jun, 2009,
12:26: PM
If p times the pth term and q times the qth term of an A.P are equal, then prove thatits (p+q)th term is zero.
Soln.
Let a and d be respetively the first term and the common diff of the A.P.
So,
pth term =a+(p-1)d
qth term =a+(q-1)d
Acc to qn
p[a+(p-1)d]=q[a+(q-1)d]
So,
a(p-q)+d[p(p-1)-q(q-1)]=0
a(p-q)+d[{(p+q)(p-q)-(p-q)]=0
(p-q)[a+d{(p+q)-1}=0
since p is not equal to q,so p-q can't b equal to zero.
so
a+d{(p+q)-1]=0
thus the (p+q)th term is equal to zero.
pl chk the qn which you have given again. However we have solved another question of similar type for you.
Answered by
| 29th Jun, 2009,
10:30: PM
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