{"id":1637,"date":"2009-10-23T15:07:48","date_gmt":"2009-10-23T20:07:48","guid":{"rendered":"http:\/\/www.bhargavs.com\/index.php\/social\/2009\/10\/a-for-effort-math-is-not-for-me\/"},"modified":"2020-10-21T15:07:04","modified_gmt":"2020-10-21T19:07:04","slug":"a-for-effort-math-is-not-for-me","status":"publish","type":"post","link":"https:\/\/bhargavs.com\/index.php\/2009\/10\/23\/a-for-effort-math-is-not-for-me\/","title":{"rendered":"A for effort! Math is (NOT) for me."},"content":{"rendered":"

Sometime ago, in one of newsletters I came across a question to find next number in series. The series was 3, 11, 20, 27, 29, 23. The next number in series needed to be found. Well, I tried as much as I can and stopped when my brain gave up on me. I was never too bright at math. I wasn\u2019t bad either but I wasn\u2019t this old either at that time.<\/p>\n

So can you help me find answer?<\/p>\n

<\/p>\n

A for effort was given to a colleague who answered this correctly and I can clearly see why. He answered it very thoroughly and I am going to publish it with due credits to him (name not published for privacy).<\/p>\n

As he wrote:<\/p>\n

\u201cThe series given was 3, 11, 20, 27, 29, 23<\/p>\n

The solution, the way I saw it was to find some function, f(x) that would equal:<\/p>\n

f(1) = 3, f(2) = 11, f(3) = 20, etc<\/p>\n

so that I could predict the value of f(7).<\/p>\n

I found the differences between each set of answers to go down 3 levels, with a shared difference of -3.\u00a0 Three levels means I need to find a third degree polynomial\u00a0 f(x) = ax^3 + bx^2 + cx + d.<\/p>\n

I then needed to find the values for a, b, c and d.\u00a0 There are 4 unknowns, so I need 4 equations.<\/p>\n

The four equations are:<\/p>\n

f(1) = a(1)^3 + b(1)^2 + c(1) + d = 3<\/p>\n

f(2) = a(2)^3 + b(2)^2 + c(2) + d = 11<\/p>\n

f(3) = a(3)^3 + b(3)^2 + c(3) + d = 20<\/p>\n

f(4) = a(4)^3 + b(4)^2 + c(4) + d = 27<\/p>\n

Using linear algebra and putting these into a matrix and reducing to echelon form, I solved for a, b, c and d.<\/p>\n

a=-1\/2, b=7\/2, c=1, d=-1<\/p>\n

That makes f(x) = -1\/2 x^3 + 7\/2 x^2 + x \u2013 1<\/p>\n

Calculating out f(x):<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
X<\/td>\n-1\/2 x^3<\/td>\n7\/2 x^2<\/td>\nX<\/td>\n-1<\/td>\nf(x)<\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n0<\/td>\n0<\/td>\n-1<\/td>\n-1<\/td>\n<\/tr>\n
1<\/td>\n-0.5<\/td>\n3.5<\/td>\n1<\/td>\n-1<\/td>\n3<\/td>\n<\/tr>\n
2<\/td>\n-4<\/td>\n14<\/td>\n2<\/td>\n-1<\/td>\n11<\/td>\n<\/tr>\n
3<\/td>\n-13.5<\/td>\n31.5<\/td>\n3<\/td>\n-1<\/td>\n20<\/td>\n<\/tr>\n
4<\/td>\n-32<\/td>\n56<\/td>\n4<\/td>\n-1<\/td>\n27<\/td>\n<\/tr>\n
5<\/td>\n-62.5<\/td>\n87.5<\/td>\n5<\/td>\n-1<\/td>\n29<\/td>\n<\/tr>\n
6<\/td>\n-108<\/td>\n126<\/td>\n6<\/td>\n-1<\/td>\n23<\/td>\n<\/tr>\n
7<\/td>\n-171.5<\/td>\n171.5<\/td>\n7<\/td>\n-1<\/td>\n6<\/span><\/b><\/td>\n<\/tr>\n
8<\/td>\n-256<\/td>\n224<\/td>\n8<\/td>\n-1<\/td>\n-25<\/td>\n<\/tr>\n
9<\/td>\n-364.5<\/td>\n283.5<\/td>\n9<\/td>\n-1<\/td>\n-73<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Finally, the answer to the question is 6, highlighted above in red.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

Sometime ago, in one of newsletters I came across a question to find next number in series. The series was 3, 11, 20, 27, 29, 23. The next number in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pgc_sgb_lightbox_settings":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[46],"tags":[113,164,244],"class_list":["post-1637","post","type-post","status-publish","format-standard","hentry","category-social","tag-effort","tag-math","tag-social"],"yoast_head":"\nA for effort! Math is (NOT) for me. - Bhargav's IT Playground<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/bhargavs.com\/index.php\/2009\/10\/23\/a-for-effort-math-is-not-for-me\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A for effort! Math is (NOT) for me. - Bhargav's IT Playground\" \/>\n<meta property=\"og:description\" content=\"Sometime ago, in one of newsletters I came across a question to find next number in series. The series was 3, 11, 20, 27, 29, 23. 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