If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.

Answer Details

Let's denote the first term of the AP by 'a', and the common difference by 'd'. We're told that the sum of the first four terms of the AP is 42, so we can write an equation: a + (a+d) + (a+2d) + (a+3d) = 42 Simplifying this equation gives: 4a + 6d = 42 2a + 3d = 21 --- equation (1) We're also told that the 7th term of the AP is twice the third term, which we can write as: a + 6d = 2(a + 2d) Simplifying this equation gives: a = 4d --- equation (2) Now we can substitute equation (2) into equation (1) to get an equation in terms of 'd' only: 2(4d) + 3d = 21 Solving for 'd', we get: d = 3 Therefore, the common difference of the AP is 3.