The 4th and 10th terms of A.P. are 13 and 25 respectively. Find its (i) first term (ii) common difference (iii) 17th term.
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Question

The 4th and 10th terms of A.P. are 13 and 25 respectively. Find its (i) first term (ii) common difference (iii) 17th term.

KnowledgeBoat · Accepted Answer

We know that, nth term of an A.P. is given by, an = a + (n - 1)d Given, 4th term is 13. ∴ a4 = a + (4 - 1)d ⇒ 13 = a + 3d ⇒ a + 3d = 13 .......(1) Given, 10th term is 25 ∴ a10 = a + (10 - 1)d ⇒ 25 = a + 9d ⇒ a + 9d = 25 ......(2) Subtracting equation (1) from (2) we get, ⇒ a + 9d - (a + 3d) = 25 - 13 ⇒ a + 9d - a - 3d = 12 ⇒ 6d = 12 ⇒ d = ⇒ d = 2. Substituting value of d in (1) we get, ⇒ a + 3(2) = 13 ⇒ a + 6 = 13 ⇒ a = 13 - 6 ⇒ a = 7. ∴ a17 = 7 + (17 - 1)2 = 7 + (16)2 = 7 + 32 = 39. Hence, a = 7, d = 2 and a17 = 39.

Mathematics

The 4th and 10th terms of A.P. are 13 and 25 respectively. Find its (i) first term (ii) common difference (iii) 17th term.

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