Question
In a 7-term number series, all the terms are in arithmetic progression. The 3rd term of the series is 17 and the 6th term is 32. What is the 7th term of the series?
Solution
Let the first term be a and common difference be d. 3rd term: a + 2d = 17 …(1) 6th term: a + 5d = 32 …(2) Subtract (1) from (2): (a + 5d) − (a + 2d) = 32 − 17 3d = 15 d = 5 From (1): a + 2×5 = 17 ⇒ a + 10 = 17 ⇒ a = 7 7th term = a + 6d = 7 + 6×5 = 7 + 30 = 37
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