The 6th term of an A.P is twice the third and the first term is 3. Find the common difference and the 10th term and find the sum of the 1st 10 terms

Answer 1

This is just a direct application of your definitions.
"the first term is 3" ---> a = 3
"The 6th term of an A.P is twice the third" ---> a+5d = 2(a+2d)
3 + 5d = 6 + 4d
d = 3
term(10) = a + 9d = ....
sum(10) = (10/2)(2a + 9d) = ...