Find the 63rd term of the following arithmetic sequence.6,  13,  20,  27,

The given sequence is an arithmetic sequence. In an arithmetic sequence, the difference between any two successive terms is constant. This difference is also known as the common difference.

Step 1: Find the common difference (d) The common difference (d) can be found by subtracting the first term from the second term. In this case, d = 13 - 6 = 7.

Step 2: Use the formula of the nth term of an arithmetic sequence The nth term (a_n) of an arithmetic sequence can be found using the formula:

a_n = a + (n - 1) * d

where: a is the first term of the sequence, n is the position of the term in the sequence, d is the common difference.

Step 3: Substitute the values into the formula Substitute a = 6, d = 7, and n = 63 into the formula:

a_63 = 6 + (63 - 1) * 7 a_63 = 6 + 62 * 7 a_63 = 6 + 434 a_63 = 440

So, the 63rd term of the given arithmetic sequence is 440.