Paragraph: Read the following information and answer Let t_n= ^n + ^n . Question: What is t₃-t₅ t₅-t₇ equal to?

Step-by-step solution

t_n= ^n + ^n Now, t₃-t₅ t₅-t₇ = ^3 + ^3 - ^5 - ^5 ^5 + ^5 - ^7 - ^7 aligned & = ^3 (1- ^2 )+ ^3 (1- ^2 ) ^5 (1- ^2 )+ ^7 (1- ^2 ) & = ^3 ^2 + ^3 ^2 ^5 ^2 + ^7 ^2 aligned aligned & = ^2 ^2 ( + ) ^2 ^2 ( ^3 + ^3 ) & = ( + ) ( ^3 + ^3 ) = t₁ t₃ aligned