If the 5th and 12th terms of an AP −4 and −18 respectively, find the sum of first 20 terms of the AP.
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Solution
Let a be the first term and d be the common difference of the given AP. Then T5 = -4 and T12 = -18
⇒a + (5 - 1) d = -4 and a + (12 - 1) d = -18 i.e., a + 4d = - 4 ...(i) also, a +11d = -18 ...(ii) On subtracting (i) from (ii), we get: 7d = -14 ⇒ d = -2 Putting d = -2 in (i), we get: a = 4 ∴ a = 4, d = -2 and n = 20 Sum of the first 20 terms =