### Video Transcript

Write an expression for the sum of
the first π terms of an arithmetic sequence with first term π and last term
π.

We know that the sum of the first
π terms of an arithmetic sequence can be calculated using the formula π over two
multiplied by two π plus π minus one multiplied by π, where π is the number of
terms, π is the first term, and π is the common difference. We also know that the πth term π
sub π is equal to π plus π minus one multiplied by π. We are told in this question that
π is the last term. Therefore, π is equal to π plus
π minus one multiplied by π. Since π plus π is equal to two
π, we can rewrite our formula for π sub π as π over two multiplied by π plus π
plus π minus one multiplied by π.

We know that the second part inside
the brackets π plus π minus one multiplied by π is equal to π. The sum of the first π terms of an
arithmetic sequence with first term π and last term π is therefore equal to π
over two multiplied by π plus π.