{"id":1050,"date":"2013-04-29t10:00:36","date_gmt":"2013-04-29t10:00:36","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=1050"},"modified":"2018-10-24t03:18:42","modified_gmt":"2018-10-24t10:18:42","slug":"sat-math-review-sequences","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/","title":{"rendered":"sat math review: sequences"},"content":{"rendered":"

you\u2019ll probably get one or two questions about sequences on your sat. since they\u2019re not a really big deal, don\u2019t start your sat studies here. instead, spend some time on the bigger issues, like sat geometry<\/a> and sat graphs<\/a>. but if you\u2019ve already mastered those, then it certainly doesn\u2019t hurt to dig into the smaller details.<\/p>\n

before getting into the sat\u2019s dirty tricks, we\u2019ll review the two basic types of sequences.<\/p>\n

 <\/p>\n

arithmetic sequences<\/h2>\n

an arithmetic sequence increases by addition. it might look like this:<\/p>\n

1, 3, 5, 7, \u2026<\/p>\n

if a <\/i>is the first term, (1 in the example), and r<\/i> is the change (2 in the example), an arithmetic sequence just adds one more r<\/i> for each term of the sequence.<\/p>\n

a<\/i>, a + r, a + 2r, a + 3r, \u2026<\/i><\/p>\n

the formula for any one term in an arithmetic sequence is an <\/sub>= a + r(n-1)<\/i>, but don\u2019t just memorize that formula. look back at that sequence of odd numbers and ask yourself why<\/i> the formula is true. you\u2019ll be much better off on your sat if you can understand how systems work. you want to be able to come up with the formula yourself without knowing it by heart.<\/p>\n

 <\/p>\n

geometric sequences<\/h2>\n

geometric sequences increase by multiplication. for example:<\/p>\n

3, 6, 12, 24, \u2026<\/p>\n

each number is the previous term multiplied by some constant. in this case, a<\/i> (the first term) is 3, and r <\/i>(the change) is 2. since you\u2019re multiplying that r<\/i> again with each term of the sequence, the change is exponential.<\/p>\n

a<\/i>, ar, ar2<\/sup>, ar3<\/sup>, \u2026<\/i><\/p>\n

again, look closely at how that example sequence represents the pattern. you should be able to create the formula yourself after spending enough time looking at the variables and the example.<\/p>\n

even though the sat doesn\u2019t require the formula to find the value of a term, just incase you\u2019re curious: an <\/sub>= ar(n-1)<\/sup><\/i><\/p>\n

 <\/p>\n

how the sat uses sequences: easier questions<\/h2>\n

if you get a sequence question early in a math section of your sat\u2014where the easy questions are\u2014it\u2019ll probably just be about finding some the value of a term in the first few numbers of a sequence. you might see something like this:<\/p>\n

1, 3, 9, x, 81,\u2026<\/i><\/p>\n

1. in the sequence above, what is the value of x?<\/i><\/p>\n

a little later on in a section, they might just throw in some simple twist<\/p>\n

x, 3, 9, y, 81,\u2026<\/i><\/p>\n

1. in the sequence above, what is the value of y\u2013x?<\/i><\/p>\n

if you don\u2019t know whether a sequence is geometric or arithmetic, you need three terms to decide. without that 81 above, this could easily have been an arithmetic sequence where x<\/i> = -3 and y <\/i>= 15.<\/p>\n

 <\/p>\n

harder sat sequences<\/h2>\n

of course, the sat likes to test your puzzle-solving abilities<\/span>, so you might get a whole \u2018nother kind of sequence with its own made up rules. in that case, those formulas won\u2019t really help. or, similarly, you might be asked how many numbers in a sequence share some property<\/a>.<\/p>\n

if you\u2019re not sure what to do, it\u2019s a good idea write out a few terms (or a few more<\/i> terms) of a sequence and look for patterns.<\/p>\n

as a matter of fact, that\u2019s a good idea when you\u2019re stuck on any<\/i> sat math problem. map out the situation<\/a> and look for a pattern.<\/p>\n

\u00a0<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

you\u2019ll probably get one or two questions about sequences on your sat. since they\u2019re not a really big deal, don\u2019t start your sat studies here. instead, spend some time on the bigger issues, like sat geometry and sat graphs. but if you\u2019ve already mastered those, then it certainly doesn\u2019t hurt to dig into the smaller […]<\/p>\n","protected":false},"author":42,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[81,61],"ppma_author":[24883],"acf":[],"yoast_head":"\nsat math review: sequences - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"sat math review: sequences\" \/>\n<meta property=\"og:description\" content=\"you\u2019ll probably get one or two questions about sequences on your sat. since they\u2019re not a really big deal, don\u2019t start your sat studies here. instead, spend some time on the bigger issues, like sat geometry and sat graphs. but if you\u2019ve already mastered those, then it certainly doesn\u2019t hurt to dig into the smaller […]\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-04-29t10:00:36+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-10-24t10:18:42+00:00\" \/>\n<meta name=\"author\" content=\"lucas fink\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:site\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:label1\" content=\"written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucas fink\" \/>\n\t<meta name=\"twitter:label2\" content=\"est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"article\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/#article\",\"ispartof\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\"},\"author\":{\"name\":\"lucas fink\",\"@id\":\"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/c06e6a007d0b81117c00610ed88b6c7d\"},\"headline\":\"sat math review: sequences\",\"datepublished\":\"2013-04-29t10:00:36+00:00\",\"datemodified\":\"2018-10-24t10:18:42+00:00\",\"mainentityofpage\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\"},\"wordcount\":553,\"commentcount\":0,\"publisher\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/#organization\"},\"keywords\":[\"sat math section\",\"sat sequences\"],\"articlesection\":[\"sat\"],\"inlanguage\":\"en-us\",\"potentialaction\":[{\"@type\":\"commentaction\",\"name\":\"comment\",\"target\":[\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/#respond\"]}]},{\"@type\":\"webpage\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\",\"url\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-math-review-sequences\/\",\"name\":\"sat math review: sequences - 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