Describe each pattern with the general term:
a. 2, 4, 6, 8 ...
b. 4, 7, 10, 13 ...
c. 1, 4, 9, 16 ...
a. The pattern in the first sequence is an arithmetic progression with a common difference of 2. Each term is obtained by adding 2 to the previous term. So the general term is given by T(n) = 2n, where n represents the nth term.
b. The pattern in the second sequence is also an arithmetic progression with a common difference of 3. Each term is obtained by adding 3 to the previous term. So the general term is given by T(n) = 3n + 1.
c. The pattern in the third sequence is a sequence of perfect squares. Each term is obtained by squaring the natural numbers. So the general term is given by T(n) = n^2.