Pre-Calculus: Series and Sequence & Pascal's Triangle

Answer the exercises:

EXERCISE 2.1 A. For each item, determine the indicated nth term given two terms of the sequence. (Hint: Find first the common difference.) 1. a, = 2, a, = 8 a 2. a, = -5, a = 3 a =PASCAL'S TRIANGLE AND THE BINOMIAL THEOREM 141 EXERCISE 2.3 A. Using Pascal's triangle, determine the following: 1. the entries in the 8th row 2. the coefficient of the third term in the expansion of (a + bj dunnor shift bitsvid). 3. the coefficient of the 5th term in the expansion of (a + b) . (ye + DE) to noiansqxe ads at unof dixie sil evit) 4. the coefficient of the sixth term in the expansion of (x + y) 5. the coefficient of the 4th term in the expansion of (x + y) 10SEQUENCE AND SERIES C. Find the sum of the first five terms of the sequence defined by each formula. 125 2. a = 1 + 5(n - 1) Caseshe just fie how sang of syed binow revely nose storfw or 3. a =-8-2(n - 1) Asoon is having womanrun 4. b = 1,800(1.05)" goingof To GoMinor 5. b = 320(0.25)" -1SEQUENCE AND SERIES 124 3. a = 7, a = 35 a We want to four Spring of the Ou following 4. a, = 6, a, = 31 a = unit offwin my sw. sonsmuse ofentine ne awolfor leowent off some as (tip - ci offfor) b bra (081 al raider) 5. a, = - 10, a, =-28 a, = HOP B. For each item, determine the indicated nth term given the first term and the common ratio of the sequence. 1. a = 2, r= 3 a2 . 2. a = 20, r= 2 as -isV meets lalot off .wold 3. a = 1,800, r = 1.05 a = 4. a = 320, r =- a 5. a = 5,000, r = W / m a 10