Determine the 30th term in an arithmetic sequence {8, 17, 26, 35 …}Also find their associated sum.

To determine the 30th term in the arithmetic sequence {8, 17, 26, 35 ...}, we need to find the common difference first. The common difference is the constant value that is added to each term to get the next term.

In this sequence, we can see that each term is obtained by adding 9 to the previous term. Therefore, the common difference is 9.

To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

In this case, the first term is 8, the common difference is 9, and we want to find the 30th term. Plugging these values into the formula, we get:

30th term = 8 + (30 - 1) * 9 = 8 + 29 * 9 = 8 + 261 = 269

So, the 30th term in the arithmetic sequence is 269.

To find the sum of the first 30 terms of the sequence, we can use the formula for the sum of an arithmetic series:

sum = (n/2) * (first term + last term)

In this case, the first term is 8, the last term is the 30th term we just found (269), and the number of terms is 30. Plugging these values into the formula, we get:

sum = (30/2) * (8 + 269) = 15 * 277 = 4155

Therefore, the sum of the first 30 terms of the arithmetic sequence is 4155.