Question
Three series I, II and III, are given below, which
contain a missing term 'P', 'Q' and 'R' respectively. Series I: 12, 13, 17, 44, P, 3425 Series II: 12.8, 32, 80, 200, 500, Q Series III: 15, 40, R, 170, 291, 460 Find the third term of a series whose first term is (P - 2R) and follows the pattern of series II.Solution
Series I: 12 + 1¹ = 13 13 + 2² = 17 17 + 3³ = 44 44 + 4⁴ = 300 300 + 5⁵ = 3425 'P' = 300 Series II: 12.8 × 2.5 = 32 32 × 2.5 = 80 80 × 2.5 = 200 200 × 2.5 = 500 500 × 2.5 = 1250 'Q' = 1250 Series III: 15 + 5² = 40 40 + 7² = 89 89 + 9² = 170 170 + 11² = 291 291 + 13² = 460 'R' = 89 'P' = 300
'R' = 89 First term of the new series = P - 2R = 300 – 2 × 89 = 300 - 178 = 122 The series follows the pattern of Series II, i.e. each term is multiplied by 2.5. Second term = 122 × 2.5 = 305 Third term = 305 × 2.5 = 762.5
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