Question
Three sequences, labeled as I,
II, and III, are provided below, with the missing terms represented by P, Q, and R, respectively. Series I: 73, 78, 88, 108, P, 228 Series II: 1296, 1274, 1230, 1164, Q, 966 Series III: 17, 25, 52, R, 241, 457 Suppose Series IV follows the same pattern as Series III and begins at 179, with the 3rd and 6th terms of Series IV represented as 'm' and 'n' respectively, determine the value of: (n + Q) - (2P + 3R)Solution
ATQ, Series I, 73 + 5 × 20 = 78 78 + 5 × 21 = 88 88 + 5 × 22 = 108 108 + 5 × 23 = 148 148 + 5 × 24 = 228 P = 148 Series II, 1296 - 22 × 1 = 1274 1274 - 22 × 2 = 1230 1230 - 22 × 3 = 1164 1164 - 22 × 4 = 1076 1076 - 22 × 5 = 966 Q = 1076 Series III, 17 + 23 = 25 25 + 33 = 52 52 + 43 = 116 116 + 53 = 241 241 + 63 = 457 R = 116 Series IV, 179 + 23 = 187 187 + 33 = 214 214 + 43 = 278 278 + 53 = 403 403 + 63 = 619 m = 214, n = 619 (n + Q) - (2P + 3R) = (619 + 1076) - (2 × 148 + 3 × 116) = 1695 - (296 + 348) = 1695 - 644 = 1051
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