Fibonacci's Story and Arithmetic Progressions
Leonardo Fibonacci (1170-1250) wasn't actually the first to discover "his" sequence - it was known in India centuries earlier! His real contribution was introducing Hindu-Arabic numerals (0,1,2,3...) to Europe, replacing clunky Roman numerals. We even celebrate Fibonacci Day on November 23rd (11/23) because of the digits 1,1,2,3.
Now let's tackle arithmetic progressions (A.P.) - sequences where you add the same number each time. Think 2, 5, 8, 11, 14... (adding 3 each time). The pattern is a, a+d, a+2d, a+3d... where 'a' is the first term and 'd' is the common difference.
Two key formulas you absolutely need: nth term: tₙ = a + n−1d and sum of n terms: Sₙ = n/22a+(n−1)d. These formulas are your best friends for solving A.P. problems quickly!
Memory Trick: The sum formula has two versions - use Sₙ = n/2firstterm+lastterm when you know both ends!