3 times the tenth term is equal to 5 times the twentieth term . find twentieth term

If the question is 3 times the tenth term is equal to 5 times the twentieth term, find thetwentieththirty fifth term then the answer is as follows:

Letaanddbe the first term and the common difference of the A.P.Given that 3a₁₀= 5a₂₀⇒3 × (a+ 9d) = 5 × (a+ 19d)⇒3a+ 27d= 5a+ 95d⇒ (5a+ 95d) (3a+ 27d) = 0⇒2a+ 68d= 0⇒2 (a+ 34d) = 0⇒a+ 34d= 0⇒a₃₅= 0Thus, the thirty fifth term of the A.P. is zero