Question
Average of four consecutive prime numbers T1, T2, T3,
and T4 is (17 + x). If the average of T1 and T2 is (13 + x) and the average of T3 and T4 is (13 + 3x), then find T4.Solution
ATQ, Sum of T1, T2, T3, and T4 = (17 + x) × 4 = 68 + 4x Sum of T1 and T2 = (13 + x) × 2 = 26 + 2x Sum of T3 and T4 = (13 + 3x) × 2 = 26 + 6x Now, setting the equations equal: 26 + 2x + 26 + 6x = 68 + 4x Or, x = 4 Sum of T3 and T4 = 26 + 6 × 4 = 50 T3, T4 = 23, 29 Answer: T4 = 29
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