Question

If pth term is q and qth term is p of an airthmetic progreaaion. then prove that ( p+ q) th term is zero.

Answer 1

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.

Answer 2

$\bf\huge\ Question:-$

If pth term is q and qth term is p of an airthmetic progreaaion. then prove that ( p+ q) th term is zero.

$\bf\huge\ Answer:-$

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