Question

The sum of the third and seventh terms of a linear sequence is 38 and the ninth term is 37.find the sequence.

Answer 1

just use your definitions
e.g.
term(3) = a + 2d , etc

a+2d + a+6d = 38
2a + 8d = 38
a + 4d = 19 ***

a + 8d = 37 **

subtract them:
4 d = 18
d = 9/2 or 4.5

into **
a + 72/2 = 37
a + 36 = 37
a = 1

the sequence is:
1 , 5.5, 10, 14.5, 19, 23.5, 28, ...