https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/sum-of-arithmetic-sequence-arithmetic-series 2022-10-07T00:22:18.752150461Z Arithmetic series intro Sal explains the formula for the sum of a finite arithmetic series Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/85b3e32a-0fa7-4f0d-950b-7ae0a2a5b525_1280_720_base.png Arithmetic series intro Sal explains the formula for the sum of a finite arithmetic series https://cdn.kastatic.org/ka-youtube-converted/cYw4MFWsB6c.mp4/cYw4MFWsB6c.mp4 236 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/formula-for-arithmetic-series 2023-04-15T06:53:33.172253602Z Arithmetic series formula Learn how to write an arithmetic sequence in general terms, using a common difference d and a first term a. Next, we'll see that this formula is equivalent to multiplying the average of the first and last terms by the number of terms. Sal Khan video https://cdn.kastatic.org/googleusercontent/qEMnOj5mahOb9mXy-3Bssf6SOGEG_ycb7kMtpRPfqRCcbcfk-E7JDi-Wg7izEpNc3kLPCn7qCX50R1FxWSDbbo8h Arithmetic series formula Learn how to write an arithmetic sequence in general terms, using a common difference d and a first term a. Next, we'll see that this formula is equivalent to multiplying the average of the first and last terms by the number of terms. https://cdn.kastatic.org/ka-youtube-converted/Uy_L8tnihDM.mp4/Uy_L8tnihDM.mp4 467 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/a/evaluating-arithmetic-series-guided-practice 2021-06-30T17:32:39Z Arithmetic series Walk through a guided practice where you'll start by finding a simple sum and end by evaluating finite arithmetic series. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/evaluating-finite-arithmetic-series 2022-10-07T00:22:18.752150461Z Worked example: arithmetic series (sigma notation) Sal evaluates the arithmetic series Σ(2k+50) for k=1 to 550. He does that using the arithmetic series formula (a₁+aₙ)*n/2. video https://cdn.kastatic.org/ka_thumbnails_cache/27bc84e6-eff8-402a-886a-abf0cf426acf_1280_720_base.png Worked example: arithmetic series (sigma notation) Sal evaluates the arithmetic series Σ(2k+50) for k=1 to 550. He does that using the arithmetic series formula (a₁+aₙ)*n/2. https://cdn.kastatic.org/ka-youtube-converted/RM644gFKo_g.mp4/RM644gFKo_g.mp4 422 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/evaluating-arithmetic-sum-example 2022-10-07T00:22:18.752150461Z Worked example: arithmetic series (sum expression) Sal evaluates the arithmetic sum (-50)+(-44)+(-38)+...+2044. He does that by finding the number of terms and using the arithmetic series formula (a₁+aₙ)*n/2. video https://cdn.kastatic.org/ka_thumbnails_cache/2d37671b-0b85-4004-8ee0-eabdfaea4e02_1280_720_base.png Worked example: arithmetic series (sum expression) Sal evaluates the arithmetic sum (-50)+(-44)+(-38)+...+2044. He does that by finding the number of terms and using the arithmetic series formula (a₁+aₙ)*n/2. https://cdn.kastatic.org/ka-youtube-converted/0-wa7voc0uM.mp4/0-wa7voc0uM.mp4 407 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/finding-sum-from-recursive-definition-of-sequence 2022-10-07T00:22:18.752150461Z Worked example: arithmetic series (recursive formula) Sal evaluates the sum of the first 650 terms in the sequence defined recursively as {aᵢ=aᵢ₋₁+11, a₁=4}. He does that by finding the 650th term and using the arithmetic series formula (a₁+aₙ)*n/2. video https://cdn.kastatic.org/ka_thumbnails_cache/8c96b871-ffd4-41ab-9224-963068b5b110_1280_720_base.png Worked example: arithmetic series (recursive formula) Sal evaluates the sum of the first 650 terms in the sequence defined recursively as {aᵢ=aᵢ₋₁+11, a₁=4}. He does that by finding the 650th term and using the arithmetic series formula (a₁+aₙ)*n/2. https://cdn.kastatic.org/ka-youtube-converted/pIO34mrW_Ro.mp4/pIO34mrW_Ro.mp4 321 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/a/evaluating-arithmetic-series-worksheet 2021-06-30T17:32:36Z Arithmetic series worksheet Try a few problems where you'll be asked to evaluate finite arithmetic series. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/e/arithmetic_series 2025-03-01T15:52:37.13987578Z Arithmetic series Practice evaluating arithmetic series using the formula (n/2)⋅(a₁+aₙ). Ben Alpert exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/v/alternate-proof-to-induction-for-integer-sum 2021-06-30T17:32:39Z Proof of finite arithmetic series formula Watch Sal prove the expression for the sum of all positive integers up to and including n. Sal Khan video https://cdn.kastatic.org/googleusercontent/kYhTpn-E91_kmCOjuOkK971BpA_ovR_UEoUBuyr7e8iXgNsSvLBVYDDLsdpJDuSldIcphPohd3JjXVLy-LbOFF9N Proof of finite arithmetic series formula Watch Sal prove the expression for the sum of all positive integers up to and including n. https://cdn.kastatic.org/ka-youtube-converted/1wnIsgUivEQ.mp4/1wnIsgUivEQ.mp4 212 Arithmetic series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:arith-series/a/series-faq 2022-10-26T00:13:38.755031109Z Series: FAQ Frequently asked questions on series article