Question

In an AP .,5 times the fifth term is equal to 7 times the seventh term. Prove that 12th term is 0.

Answer 1

     

$5 \times T_5=7 \times T_7 \\ \\ \Rightarrow\ 5(a+4d)=7(a+6d) \\ \\ \Rightarrow\ 5a+20d = 7a+42d \\ \\ \Rightarrow\ 7a+42d-5a-20d=0 \\ \\ \Rightarrow\ 2a+22d=0 \\ \\ \Rightarrow\ 2(a+11d)=0 \\ \\ \Rightarrow\ 2\times T_{12}=0 \\ \\ \Rightarrow\ T_{12}=0/2 \\ \\ \Rightarrow\ T_{12}=0$

Hence proved!

Plz ask me if you have any doubt on my answer.

Thank you. :-))

     

Answer 2

Heya!!!

Here's your answer...