ПОВТОРЕННЯ НАВЧАЛЬНОГО МАТЕРІАЛУ » §.3 (2.5)

5. (xn): xn = 12n – 18. S20 – ? S20 = (2x_1+ 19d)/2 • 20 = 20x1 + 19d. x1 = 12 • 1 – 18 = –6 x2 = 24 – 18 = 6. d = x2 – x1 = 6 + 6 = 12. S20 = 20 • (–6) + 190 • 12 = 2160. Sm = 480; m – ? Sm = (2 •(-6)+ 12 •(m-1))/2 • m = (-12+12m-12)/2 • m = (6m – 12) • m = 6m2 – 12m = 480. m2 – 2m – 80 = 0. m1 = 10; m2 –8 < 0. m = 10. Sk – найм. – ?; К – ? Sk = bk2 – 12k; лін. зн. – 12 при к = 1. 6. (yn): S7 = 3,5; S10 = 42,5 y1, d, y13 – ? S10 – S7 = y8 + y9 + y10 = 42,5 – 3,5 = 39. y1 = 7d + y1 + 8d + y1 + 9d = 39. 3y1 + 24d = 39. y1 + 8d = 13. S7 = (2y_1+ 6d)/2 • 7 = 3,5; (y1 + 3d) • 7 = 3,5. y1 + 3d = 0,5. y1 + 8d = 13. y1 = 13 – 8 • 25 = –187. y1 + 3d = 0,5. y13 = y1 + 12d = –187 + 300 = 113. 5d = 12,5, d = 25.