An arithmetic sequence has a common difference of 10 and its 6th term is 52. Find its 30th term.

Sure, here's how you can find the 30th term of the arithmetic sequence:

Step 1: Identify the common difference (d) and the value of the 6th term (a6). From the problem, we know that d = 10 and a6 = 52.

Step 2: Use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d. But we don't know the first term (a1) yet.

Step 3: To find the first term (a1), we can rearrange the formula from step 2 to solve for a1: a1 = an - (n-1)d. Substituting the known values, we get a1 = a6 - (6-1)d = 52 - 5*10 = 2.

Step 4: Now that we know a1, we can find the 30th term (a30) by substituting the values into the formula from step 2: a30 = a1 + (30-1)d = 2 + 29*10 = 292.

So, the 30th term of the arithmetic sequence is 292.