1, if in an a.p ,mtm=ntn then show that tm+n=0

2. 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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