{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Arithmetic (Linear) Sequences' data-url='/boclips/videos/634c049af0c50125a1d07068' data-video-url='/boclips/videos/634c049af0c50125a1d07068' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nArithmetic (Linear) Sequences\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356647\" href=\"/search?publisher_ids%5B%5D=30356647\u0026amp;search_tab_id=2\"\u003eFuseSchool\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eIn this video we are going to look at arithmetic sequences in more detail. These are also known as linear sequences.We will discover how to find the nth term rule, which we will then use to find any term in the sequence.Before we start,...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eIn this video we are going to look at arithmetic sequences in more detail. These are also known as linear sequences.\u003cbr/\u003e\u003cbr/\u003eWe will discover how to find the nth term rule, which we will then use to find any term in the sequence.\u003cbr/\u003e\u003cbr/\u003eBefore we start, you should already know that each number in the sequence is called a term. This is the first term, Second term and so on.\u003cbr/\u003e\u003cbr/\u003eAnd that this just tells us that the sequence carries on forever.\u003cbr/\u003e\u003cbr/\u003eArithmetic sequences have a common difference. This means that they always go up by the same amount. So the common difference for this sequence is 3. \u003cbr/\u003e\u003cbr/\u003eThe nth term for this sequence is 3n + 2. We can use this to generate the sequence. The n stands for what term it is.\u003cbr/\u003e\u003cbr/\u003eThe first term, n is 1. Substitute 1 into the formula. \u003cbr/\u003e3 times 1 plus 2, for the second term, substitute n equals 2 into the formula, for the 5th term, substitute in n equals 5. We can choose any term… the 100th. \u003cbr/\u003e\u003cbr/\u003eHere’s a question for you to. Pause the video, generate the sequence and click play when you’re ready. Look at these two sequences.\u003cbr/\u003e\u003cbr/\u003eA sequence has an nthterm of -5n + 50\u003cbr/\u003eFind the first 5 terms.\u003cbr/\u003e\u003cbr/\u003e1st term = -5(1) + 50 = 45 \u003cbr/\u003e2nd term = -5(2) + 50 = 40\u003cbr/\u003e3rd term = -5(3) + 50 = 35\u003cbr/\u003e4th term = -5(4) + 50 = 30\u003cbr/\u003e5th term = -5(5) + 50 = 25\u003cbr/\u003e\u003cbr/\u003e45, 40, 35, 30, 25, ...\u003cbr/\u003e\u003cbr/\u003eWhat do you notice about the common difference and the nth term rule? For arithmetic sequences, the number in front of the ‘n’ is ALWAYS the common difference. So because the common difference was minus 5, the nth term rule is minus 5n. \u003cbr/\u003e\u003cbr/\u003eGiven these 3 sequences, what numbers are missing from their nth term rules? Difference of 4, so the formula is 4n. Difference of minus 3 so the formula is -3n. Difference of half so formula is 0.5n.\u003cbr/\u003e\u003cbr/\u003eNow looking at the numbers after the n’s… where do these come from?\u003cbr/\u003e\u003cbr/\u003eHow do you go from plus 4 to 2? You have to subtract 2. From -3 to 22 you have to add 25. From 0.5 to 1.5 you add 1. And there you have the nth term rule. \u003cbr/\u003e\u003cbr/\u003eHere are some questions for you to do. Pause the video, work them out and click play when you’re ready.\u003cbr/\u003e\u003cbr/\u003eThat’s nearly everything you need to know about arithmetic sequences. \u003cbr/\u003eYou can now find the nth term rule, you know how to generate a sequence from the rule, and you can find any term in the sequence.\u003cbr/\u003e\u003cbr/\u003eAll that is left is to discover how we work out if a number is in sequence or not - watch part 2 for that. \u003cbr/\u003e\u003cbr/\u003eCREDITS\u003cbr/\u003eAnimation \u0026 Design: Waldi Apollis\u003cbr/\u003eNarration: Lucy Billings\u003cbr/\u003eScript: Lucy Billings\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv 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