A linear equation has terms: a+2b, a + 6b, a + 10b, ......., ........ the second term equals 8 and the fifth term equals 44. Work out the value of a & b

We are given the second term both as a number and an equation, so we can saya + 6b = 8We can then estimate the fifth term by continuing the pattern of adding 4b to each term in the sequence, which gives:Third term = a + 10bfourth term = a + 14bfifth term - a + 18bwe can then do the same trick as above and say:a +18b = 44Now we have 2 equations we can solve simultaneously:a + 6b = 8 (1)a + 18b = 44 (2)The easiest common value to get rid of between the two equations is a, so we simply subtract equation (1) from equation (2) a + 18b = 44- a + 6b = 8Doing this term by term gives:a -a = 018b - 6b = 12b44 - 8 = 36so now we have a new equation:12b = 36to isolate b we need to divide by 12, which gives b = 3we can then substitute this into equation (1) or (2) to find aa + 6b = 8a + (63) = 8a + 18 = 8a = -10we can then check our answer by doing the same with the other equationa + 18b = 44a + (183) = 44a + 54 = 44a = -10the answers are the same so we know our answer is correct,a = -10b =3