For any AP show that `a_p+a_(p+2q)=2a_(p+q)`

For an A.P., show that T_p+T_(p+2q)=2T_(p+q) .

If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show that the sum of (p + q) terms is (p+q)/2[(a + b) + (a- b)/(p - q)] .

let a_(1),a_(2),a_(3),........., be an AP such that (a_(1)+a_(2)+a_(3)+.........+a_(p))/(a_(1)+a_(2)+a_(3)+.........+a_(q))=(p^(3))/(q^(3))(p!=q) then find (a_(6))/(a_(21))=?

Statement -1: There exists no A.P. whose three terms are sqrt(3),sqrt(5)andsqrt(7) . Statement-2: If a_(p),a_(q)anda_(r) are three distinct terms of an A.P., then (a_(p)-a_(q))/(a_(p)-q_(r)) is a rational number.

Statement -1: There exists no A.P. whose three terms are sqrt(3),sqrt(5)andsqrt(7) . Statement-2: If a_(p),a_(q)anda_(r) are three distinct terms of an A.P., then (a_(p)-a_(q))/(a_(p)-q_(r)) is a rational number.

If a_(1),a_(2),a_(3)............ are in A.P. such that a_(4)-a_(7),+a_(10)=m, then sum of 13 terms of this A.P., is;

If a, b, c be respectively the sums of p, q, r terms of an A.P., show that, (a)/(p)(q-r) + (b)/(q)(r-p) +(c )/(r )(p-q) = 0

If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G.P. are in G.P.

let a_(1),a_(2),a_(3)...... be an AP such that (a_(1)+a_(2)+............+a_(p))/(a_(1)+a_(2)+............+a_(q))=(p^(3))/(q^(3)) then a_(/)a_(21)

If a_(1),a_(2),a_(3), ……….. Are in A.P. such that a_(4)/a_(7) = 3/2 , then the 13^(th) term of the A.P. is …………..