The first four terms of the arithmetic series can be represented by a, a+x, a+2x, a+3x. These add up to 4a+6x. Their mean (average) is (4a+6x)/4=77. The 5th and 6th terms are a+4x and a+5x which add up to 2a+9x. The mean of the first 6 terms is given by (4a+6x+2a+9x)/6=77+32=109=(6a+15x)/6. So we can write two equations with two unknowns, a and x: 4a+6x=308 and 6a+15x=654. The first equation can be divided through by 2: 2a+3x=154, and then multiplied through by 3: 6a+9x=462 so 6a=462-9x, and this can be substituted in the other equation: 462-9x+15x=654. So 6x=192, from which x=32. Substitute this value in either equation: 2a+96=154, so 2a=58 and a=29. The first term, a, is therefore 29. (The series is: 29, 61, 93, 125, 157, 189.)