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

To start with, we need to notice the difference between each of the terms in the sequence. As this is a linear sequence, the sequence increases or decreases by the same amount between each term. In this question, we see that 4b is added between each term so the 4th term would be a+14b and the 5th term is a+18b.Now we need to look at the information we have been given in the question, we know that the second term a+6b is equal to 8 and the fifth term a+18b is equal to 44. So we label a+6b=8 as equation 1 and a+18b=44 as equation 2.Now we solve these simultaneous equations: Rearrange equation 1 to get a=8-6b and then sub this expression for a into equation 2 so get (8-6b)+18b=44 which rearranges to 12b=36 (by collecting the terms of b and subtracting 8 from each side). Then we have that b=3 by dividing each term by 12 and then substituting this value of b into equation 1 so that a+(6x3)=8 so a+18=8. Then subtracting 18 from both sides gives a= -10.So we have a=-10 and b=3