3. Use deductive reasoning to prove the following statements. a) The sum of any three consecutive even numbers is divisible by six.

Let in the first even number
2n+2: the second even number
2n +4: the third
even number

b) The sum of any three odd numbers is an odd number.
Let 2rn -1 = the first odd number
Let 2m- 1 = the second odd number
Let 2p-1 = the third odd number

c) a product of any two odd numbers is an odd number.

d) the difference of the sequence of two consecutive even numbers is divisible by four

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kpa and 17°c. this system uses a regenerator as well as reheating and intercooling – the intercooler returns the air to the inlet temperature. the pressure ratio across each compressor is 4 ; 300 kj/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20°c. determine the system’s thermal efficiency. assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature. (0.378)