Question
Consider the sequence: 4, 9, 11, 20, 18, 33,
? I: Terms at odd positions (1st, 3rd, 5th, 7th, …) form an arithmetic progression. II: Terms at even positions (2nd, 4th, 6th, 8th, …) form a sequence whose consecutive differences are 11, 13, 15, 17, … respectively. What is the 7th term of the sequence?Solution
ATQ, Odd-position terms: Position 1: 4 Position 3: 11 Position 5: 18 Position 7: ? Check differences: 11 − 4 = 7 18 − 11 = 7 So odd-position terms form an A.P. with common difference 7. Thus the 7th term (4th term of this A.P.) is: 4 + 3·7 = 4 + 21 = 25 Even-position terms (2nd, 4th, 6th, …) are: 9, 20, 33, … Differences: 20 − 9 = 11 33 − 20 = 13 This matches Condition II as a consistency check, but we only needed odd positions to find the 7th term. Hence, the 7th term is 25.
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