The 7th term of an A.P. is -4 and its 13th term is -16. Find its (i) first term (ii) common difference (iii) nth term.
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The 7th term of an A.P. is -4 and its 13th term is -16. Find its (i) first term (ii) common difference (iii) nth term.

KnowledgeBoat · Accepted Answer

Let first term be a and common difference be d. We know that, nth term of an A.P. is given by, an = a + (n - 1)d Given, 7th term is -4. ∴ a7 = a + (7 - 1)d ⇒ -4 = a + 6d ⇒ a + 6d = -4 ....(1) Given, 13th term is -16 ∴ a13 = a + (13 - 1)d ⇒ -16 = a + 12d ⇒ a + 12d = -16 ....(2) Subtracting (1) from (2) we get, ⇒ a + 12d - (a + 6d) = -16 - (-4) ⇒ a + 12d - a - 6d = -16 + 4 ⇒ 6d = -12 ⇒ d = ⇒ d = -2. Substituting value of d in (1) we get, ⇒ a + 6(-2) = -4 ⇒ a - 12 = -4 ⇒ a = -4 + 12 ⇒ a = 8. ∴ an = 8 + (n - 1)(-2) = 8 - 2n + 2 = 10 - 2n. Hence, a = 8, d = -2 and an = 10 - 2n.

Mathematics

The 7th term of an A.P. is -4 and its 13th term is -16. Find its (i) first term (ii) common difference (iii) nth term.

AP

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