Question
In an arithmetic progression, the 4th term is 23 and the
9th term is 48. What is the sum of the first 20 terms?Solution
ATQ, Let first term = a, common difference = d. 4th term: a + 3d = 23 9th term: a + 8d = 48 Subtract: (a + 8d) − (a + 3d) = 48 − 23 5d = 25 ⇒ d = 5. Then a = 23 − 3d = 23 − 15 = 8. Sum of first 20 terms: Sₙ = n/2 [2a + (n − 1)d] S₂₀ = 20/2 [2·8 + 19·5] = 10 [16 + 95] = 10 × 111 = 1110.
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