Question Video: Writing an Expression for the Sum of the First 𝑛 Terms of an Arithmetic Sequence Mathematics

Write an expression for the sum of the first 𝑛 terms of an arithmetic sequence with first term π‘Ž and last term 𝑙.

01:30

Video Transcript

Write an expression for the sum of the first 𝑛 terms of an arithmetic sequence with first term π‘Ž 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 π‘Ž plus 𝑛 minus one multiplied by 𝑑, where 𝑛 is the number of terms, π‘Ž is the first term, and 𝑑 is the common difference. We also know that the 𝑛th term π‘Ž sub 𝑛 is equal to π‘Ž plus 𝑛 minus one multiplied by 𝑑. We are told in this question that 𝑙 is the last term. Therefore, 𝑙 is equal to π‘Ž plus 𝑛 minus one multiplied by 𝑑. Since π‘Ž plus π‘Ž is equal to two π‘Ž, we can rewrite our formula for 𝑆 sub 𝑛 as 𝑛 over two multiplied by π‘Ž plus π‘Ž plus 𝑛 minus one multiplied by 𝑑.

We know that the second part inside the brackets π‘Ž 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 π‘Ž and last term 𝑙 is therefore equal to 𝑛 over two multiplied by π‘Ž plus 𝑙.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.