### Video Transcript

Find the sum of the first 17 terms of the arithmetic series 12 plus 21 plus 30 plus ...

The formula to calculate the sum of the first 𝑛 terms of any arithmetic series is 𝑛 divided by two multiplied by two 𝑎 plus 𝑛 minus one multiplied by 𝑑, where 𝑎 is the first term and 𝑑 is the common difference.

In our example, the sum of the first 17 terms can be calculated by dividing 17 by two and multiplying this by two 𝑎 plus 16𝑑. The first term of the series is 12. Therefore, 𝑎 is equal to 12. And the difference between each term in the series is nine. So 𝑑 is equal to nine.

Substituting in these values gives 𝑆 of 17. The sum of the first 17 terms is equal to 17 divided by two multiplied by two multiplied by 12 plus 16 multiplied by nine. 17 divided by two is 8.5, two multiplied by 12 is 24, and 16 multiplied by nine is 144. We’re then left with 8.5 multiplied by 24 plus 144. As 24 plus 144 is 168, we need to multiply 8.5 by 168. This gives us an answer of 1428.

The sum of the first 17 terms of the arithmetic series starting 12, 21, and 30 is 1428.