Find the number of terms in each of the following APs : (i) 7, 13, 19, ......., 205 (ii) 18, 15 (1/2), 13,.., -47

Question

KnowledgeBoat · Accepted Answer

(i) Given, 7, 13, 19, ......., 205. In the above A.P., First term (a) = 7 and common difference (d) = 13 - 7 = 6. Let nth term be 205. By formula, a_n = a + (n - 1)d Substituting values we get : ⇒ 205 = 7 + 6(n - 1) ⇒ 205 = 7 + 6n - 6 ⇒ 205 = 6n + 1 ⇒ 6n = 205 - 1 ⇒ 6n = 204 ⇒ n = = 34. Hence, number of terms = 34. (ii) Given, 18, In the above A.P., First term (a) = 18, Common difference (d) = . Let nth term be -47. By formula, a_n = a + (n - 1)d Substituting values we get : ⇒ -47 = ⇒ -47 = ⇒ -47 = ⇒ -94 = 41 - 5n ⇒ 5n = 41 + 94 ⇒ 5n = 135 ⇒ n = = 27. Hence, no. of terms = 27.

Mathematics

Find the number of terms in each of the following APs : (i) 7, 13, 19, ......., 205 (ii) 18, 15 (1/2), 13,.., -47

AP

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