Question
In an arithmetic progression (A.P.), the 10th term is 32
and the sum of the first 20 terms is 670. What is the first term of the A.P.?Solution
ATQ, Let first term = a, common difference = d. T10 = a + 9d = 32 ...(1) S20 = (20/2)[2a + (20 − 1)d] = 10(2a + 19d) = 670 => 2a + 19d = 67 ...(2) From (1): a = 32 − 9d. Substitute into (2): 2(32 − 9d) + 19d = 67 64 − 18d + 19d = 67 64 + d = 67 ⇒ d = 3. Then a = 32 − 9×3 = 32 − 27 = 5.
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