The 5th term of an arithmetic progression is 23 and the 12th term is 37.find the third term and common different

2 answers

Just use your definitions:
"5th term of an arithmetic progression is 23"
---> a + 4d =23
"the 12th term is 37" --> a + 11d = 37

You have two equations in two unknows.
Solve them.
Hint: I would subtract one from the other.
Let me know what you get.
a + 4d=23
a + 11d=37
a + 7d=14
a +7d÷7 =14÷7
1a + d =2