1, if in an a.p ,mtm=ntn then show that tm+n=02. if the pth term of an a.p is q and the qth term is p , then find its (p+q) th term.3. prove that for all finite values of a and b(a-b)², (a+b)²,a²+b² are in a.p.4. in the arithmatic sequence 3,7,11, 15............ and 2,5,8..........each continued to 100 terms ,find how many terms are identical.

Dear sougata

Ist question is not clear

2nd question:

let first term is =a  and common difference =d

p =a+(q-1)d  ............1

q =a+(p-1)d  ..............2

1-2

p-q = (q-p)d

d =-1

put value of d in equation 1

a =p+q -1

now p+q th term  = a+ ( p+q -1)d

                         = p+q -1 + ( p+q -1)*(-1)

                        =0

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