Video Transcript
Write an expression for the sum of
the first 𝑛 terms of an arithmetic sequence with first term 𝑎 and last term
𝑙.
We know that the sum of the first
𝑛 terms of an arithmetic sequence can be calculated using the formula 𝑛 over two
multiplied by two 𝑎 plus 𝑛 minus one multiplied by 𝑑, where 𝑛 is the number of
terms, 𝑎 is the first term, and 𝑑 is the common difference. We also know that the 𝑛th term 𝑎
sub 𝑛 is equal to 𝑎 plus 𝑛 minus one multiplied by 𝑑. We are told in this question that
𝑙 is the last term. Therefore, 𝑙 is equal to 𝑎 plus
𝑛 minus one multiplied by 𝑑. Since 𝑎 plus 𝑎 is equal to two
𝑎, we can rewrite our formula for 𝑆 sub 𝑛 as 𝑛 over two multiplied by 𝑎 plus 𝑎
plus 𝑛 minus one multiplied by 𝑑.
We know that the second part inside
the brackets 𝑎 plus 𝑛 minus one multiplied by 𝑑 is equal to 𝑙. The sum of the first 𝑛 terms of an
arithmetic sequence with first term 𝑎 and last term 𝑙 is therefore equal to 𝑛
over two multiplied by 𝑎 plus 𝑙.
