https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-arithmetic-sequences/v/arithmetic-sequences 2021-06-30T17:32:39Z Intro to arithmetic sequences Sal introduces arithmetic sequences and their main features, the initial term and the common difference. He gives various examples of such sequences, defined explicitly and recursively. Sal Khan video https://cdn.kastatic.org/googleusercontent/OrgsHeMoJUc6-j5RLRoUIVcaYF-Q39nGk23bLLQKOPj4-e45JJZypOWsNNXFilJ9aITPS6AX4kJKgtfWn7HFcAlI Intro to arithmetic sequences Sal introduces arithmetic sequences and their main features, the initial term and the common difference. He gives various examples of such sequences, defined explicitly and recursively. https://cdn.kastatic.org/ka-youtube-converted/_cooC3yG_p0.mp4/_cooC3yG_p0.mp4 427 Sequences and Series https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:constructing-arithmetic-sequences/v/explicit-formulas-for-arithmetic-sequences 2022-10-06T23:01:00.745424633Z Explicit formulas for arithmetic sequences Sal finds explicit formulas of arithmetic sequences given the first few terms of those sequences. He also explores equivalent forms of such formulas. video https://cdn.kastatic.org/ka_thumbnails_cache/648ffef4-6cad-40b4-bef8-6e92ac624996_1280_720_base.png Explicit formulas for arithmetic sequences Sal finds explicit formulas of arithmetic sequences given the first few terms of those sequences. He also explores equivalent forms of such formulas. https://cdn.kastatic.org/ka-youtube-converted/ViLt2WI0XSg.mp4/ViLt2WI0XSg.mp4 377 Sequences and Series https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:general-sequences/v/sequences-and-domain 2022-10-06T23:01:00.745424633Z Sequences and domain We can generate the same sequence with different functions and different domains. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/f363c937-b5e9-4925-968a-e5102b74ddf0_1280_720_base.png Sequences and domain We can generate the same sequence with different functions and different domains. https://cdn.kastatic.org/ka-youtube-converted/TymkzM7J1PY.mp4/TymkzM7J1PY.mp4 376 Sequences and Series https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum 2021-06-30T17:32:38Z Summation notation Sigma, Σ, is the standard notation for writing long sums. Learn how it is used in this video. Sal Khan video https://cdn.kastatic.org/googleusercontent/AkUo89aMk-ZXH2KwZTUALeYknZORIY--gS_3ht52xZLOfQSEU8xfeGgm3Ohz0IeLeNCwAh0j_7M_tfBySGHDGA Summation notation Sigma, Σ, is the standard notation for writing long sums. Learn how it is used in this video. https://cdn.kastatic.org/ka-youtube-converted/5jwXThH6fg4.mp4/5jwXThH6fg4.mp4 267 Sequences and Series https://www.khanacademy.org/math/integral-calculus/ic-series/ic-represent-func-as-series/v/writing-series-sigma-notation 2020-09-27T22:59:01Z Converting explicit series terms to summation notation Some sums are really long, but we can use sigma notation to write them in a shorthand way. See such an example here. Sal Khan video https://cdn.kastatic.org/googleusercontent/DnwmdpIJmJV_VSueuSPLMqdAXUgjRZzQmbr1Zm1eJCDYjZuu_fndndfYfUTZV54NX-WVRPaosA2_15NQz44_iMp_ZA Converting explicit series terms to summation notation Some sums are really long, but we can use sigma notation to write them in a shorthand way. See such an example here. https://cdn.kastatic.org/ka-youtube-converted/0DBDuNYsciY.mp4/0DBDuNYsciY.mp4 196 Sequences and 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 Sequences and Series https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-geometric-sequences/v/geometric-sequences-introduction 2021-06-30T17:32:40Z Intro to geometric sequences Sal introduces geometric sequences and their main features, the initial term and the common ratio. Sal Khan video https://cdn.kastatic.org/googleusercontent/EGwJyoWiNK9S9o40xAqCEN70zhYCxmMpzmSCp5vp890CX6dQLAk-NetWrz9x17rxaUPCwwEGRpjxhQT_2WdqYjk Intro to geometric sequences Sal introduces geometric sequences and their main features, the initial term and the common ratio. https://cdn.kastatic.org/ka-youtube-converted/pXo0bG4iAyg.mp4/pXo0bG4iAyg.mp4 645 Sequences and Series https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-geometric-sequences-review/v/geometric-sequences 2021-04-21T12:01:46Z Intro to geometric sequences (advanced) Sal introduces geometric sequences and gives a few examples. Notation used in this video is relatively advanced. Sal Khan video https://cdn.kastatic.org/googleusercontent/W9qzhM4EKA5aTH7RKXe-C1LbvwXtducqa6qbG7RRhZMLijoSeFPJczsw-H4eglFmCGA4zUOpEXwESCONZpzSkgeP Intro to geometric sequences (advanced) Sal introduces geometric sequences and gives a few examples. Notation used in this video is relatively advanced. https://cdn.kastatic.org/ka-youtube-converted/dIGLhLMsy2U.mp4/dIGLhLMsy2U.mp4 399 Sequences and Series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:geo-series/v/series-as-sum-of-sequence 2020-11-10T16:09:48Z Geometric series intro A geometric series is the sum of the terms of a geometric sequence. Learn more about it here. Sal Khan video https://cdn.kastatic.org/googleusercontent/TmSdYcKy73Yzh2Lwlb3RhiRliE_Ippk6x9DIoAtEk2197evzFXj08U7DSr91qZTj072cpqND7DIf_hRnrG9-NjwG Geometric series intro A geometric series is the sum of the terms of a geometric sequence. Learn more about it here. https://cdn.kastatic.org/ka-youtube-converted/rcRg_gO7-7E.mp4/rcRg_gO7-7E.mp4 173 Sequences and Series https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:geo-series-notation/v/example-finding-sum-of-finite-geometric-series 2022-10-07T00:22:18.752150461Z Worked example: finite geometric series (sigma notation) Sal evaluates the geometric series Σ2(3ᵏ) for k=0 to 99 using the finite geometric series formula a(1-rⁿ)/(1-r). video https://cdn.kastatic.org/ka_thumbnails_cache/141f5f44-3e3e-41de-87b2-89e059c39be5_1280_720_base.png Worked example: finite geometric series (sigma notation) Sal evaluates the geometric series Σ2(3ᵏ) for k=0 to 99 using the finite geometric series formula a(1-rⁿ)/(1-r). https://cdn.kastatic.org/ka-youtube-converted/AXP5PGSaaYk.mp4/AXP5PGSaaYk.mp4 168 Sequences and Series https://www.khanacademy.org/math/ka-revision-class-11-math/x64e5efbb29d87707:week-2-revision-ncert-class-11-math/x64e5efbb29d87707:sequences-and-series-revision-ncert-class-11-math/e/revision-sequences-and-series-ncert-class-11-math 2026-04-08T01:15:04.085520103Z Revision Sequences and Series Practice problems for revision of Sequences and Series. Satya Swaroop exercise