A linear sequence starts a + 2b, a + 6b, a + 10b, …….. …….. The 2nd term has value 8. The 5th term has value 44. Work out the values of a and b.

First we need to find the fourth and fifth term. So between first and second term we've added 4b, the same between the second and third term. To get to the fourth term we'd add 4b again to get a+14b, then add 4b to get the fifth term: a+18b. So now we know the second term: a+6b = 8 and a+18b = 44. To work out values of a and b we can use both these algebraic equations.So algebraically, the difference between a+6b and a+18b is of 12b and numerically the difference is 36. So 12b = 36, which means b=3. We can substitute this back into the equation a+6b=8, to find a+(6x3)=8 --> a+18 = 8 --> so a = -10 (minus 10). We can check using the second equation: -10+(18x3) = -10+54 = 44, so this is correct.