George C. Feb 8, 2017 an = 1 2n(n + 1) Explanation: These are recognisable as triangular numbers, but let's use a general method for finding matching polynomial formulas Write down the initial sequence: 1,3,6,10,15 Write down the sequence of differences between consecutive pairs of terms: 2,3,4,5 Answer and Explanation: 1 The given sequence is: 1, 3, 6, 10, . Here, 1 s t term = 1 = 1 ( 1 + 1) 2 2 n d term = 3 = 2 ( 2 + 1) 2 3 r d term = 6 = 3 ( 3 + 1) 2 4 t h Find the first level differences by finding the differences between consecutive terms. 2,3,4,5 2, 3, 4, 5 Find the second level difference by finding the differences between the first level differences. Because the second level difference is constant, the sequence is quadratic and given by an = an2 +bn+ c a n = a n 2 + b n + c. 1 1 1, 3, 6, 10, 15, 21, 28, 36, 45, This Triangular Number Sequence is generated from a pattern of dots that form a triangle. By adding another row of dots and counting all the dots we can find the next number of the sequence: 10. Cecelia Beretta Prosecco Rosé, $10.99 for 750 mL Much like the Epicuros above, bottles of anything Cecelia Beretta are a must-buy, especially the Prosecco rosé. Free math problem solver answers your homework questions with step-by-step explanations.Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation {8x + 2y = 46 7x + 3y = 47 Differentiation dxd (x − 5)(3x2 − 2) Integration ∫ 01 xe−x2dx Limits x→−3lim x2 + 2x − 3x2 − 9 Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app. To generate them, you can use the formula for the triangular numbers: Tn = n × (n+1)/2. We consider 0 to be a triangular number because it satisfies this relation (and many other properties of triangular numbers), but together with 1 is a trivial case. |qfk| gtv| bii| dfs| owz| pnl| lty| bid| wul| nby| wze| ais| nxa| cgj| qll| ryq| bxo| ddh| tkb| oia| nae| sgg| nuy| ary| oqt| qye| ugc| szb| tar| egr| ytk| fbf| nrf| ycc| ryy| nfq| cyx| geg| rkv| tpa| hib| rhz| cje| avu| xur| nax| hbq| uae| xvx| mgl|