a) Dane: (S2) = - 24 (a2) = 12 (a1) = ? r = ? (S2) = 0,5[(a1) + (a2)] *2 (S2) = (a1) + (a2) (a1) = (S2) - (a2) (a1) = - 24 - 12 (a1) = - 36 (a2) = (a1) + r r = (a2) - (a1) r = 12 - ( - 36) r = 12 + 36 r = 48 Odp: Pierwszy wyraz ciągu arytmetycznego wynosi - 36, natomiast jego różnica wynosi 48. b) Dane: (S2) = 13 (S3) = 16 (S2) = 0.5[(a1) + (a2)]*2 (S2) = (a1) + (a2) (a2) = (a1) + r (S2) = (a1) + (a1) + r (S2) = 2(a1) + r (S3) = 0,5[(a1) + (a3)]*3 (S3) = 1,5[(a1) + (a3)] (a3) = (a1) + 2r (S3) = 1,5[(a1) + (a1) + 2r] (S3) = 1,5[2(a1) + 2r] (S3) = 3(a1) + 3r { 2(a1) + r = 13 { 3(a1) + 3r = 16 { r = 13 - 2(a1) { 3(a1) + 3*[13 - 2(a1)] = 16 { 3(a1) + 39 - 6(a1) = 16 { r = 13 - 2(a1) { - 3(a1) = 16 - 39 { r = 13 - 2(a1) { - 3(a1) = - 23 /:( - 3) { r = 13 - 2(a1) { (a1) = 23/3 { r = 13 - 46/3 { (a1) = 23/3 { r = - 7/3 Odp: Pierwszy wyraz ciągu arytmetycznego wynosi - 23/3, natomiast jego różnica wynosi - 7/3. c) Dane: (a2) = 204 (a3) = - 68 (a1) = ? (a4) = ? (a3) - (a2) = r r = - 68 - 204 r = - 272 (a2) - (a1) = r 204 - (a1) = - 272 (a1) = 204 + 272 (a1) = 476 (a4) = (a1) + 3r (a4) = 476 + 3*( - 272) (a4) = 476 - 816 (a4) = - 340 Odp: Pierwszy wyraz ciśgu arytmetycznego wynosi 476, a wyraz czwarty wynosi - 340.
a) S2 = -24 a2 =12 S2 = a1 + a2 a1 +a2 = -24 a1 +12 = -24 a1 = -36 r = a2 - a1 r =12 -(-36) r = 48 Odp.:a1 = -36; r = 48 b) S2 = a1 +a1 +r S3 = 3a1 +3r 2a1 + r =13 3a1 +3r =16 r =13 -2a1 3a1 +3(13-2a1) =16 3a1 +39 - 6a1 =16 3a1 =23 a1 =23/3 r =13 - 23/3 r = -7/3 Odp.: a1 =23/3; r = -7/3 c) a1, 204, (-68),a4 r = -68 -204 r = -272 a2 -a1 =r 204 -a1 = -272 a1 =204 +272 a1 = 476 Odp.: a1 = 476; r = -272
