A linear sequence begins: a + 2b, a + 6b, a + 10b, ..., ... Given that the 2nd term has a value of 8 and the 5th term has a value of 44, calculate the values for a and b

This is a linear sequence which we can see increasing by 4b with every consecutive term.

Given the values of the first 3 terms, we can see that the 4th and 5th terms must be a + 14b and a + 18b respectively.Since we know that the 2nd term must be equal to 8 and the 5th term must be equal to 44, we can form a pair of simultaneous equations: a + 6b = 8 and a + 18b = 44

Subtracting the first equation from the second one we get 12b = 36, which rearranges to get b = 3.

Substituting this value for b back into the first equation we get a + 18 = 8, which rearranges to get a = -10.

We now have both of the values we were asked to find in the question, a = -10 and b = 3.