Which term of the A.P. (i) 3, 8, 13, 18, ... is 78 ? (ii) is -47 ?

Question

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(i) The given A.P. is 3, 8, 13, 18 .... Here, first term = a = 3 and common difference = d = 8 - 3 = 5. Let 78 be nth term of the A.P., or a_n = 78 The nth term of A.P. is given by a_n = a + (n - 1)d Putting value of d and a_n in above equation we get, ⇒ a_n = a + (n - 1)d ⇒ 78 = 3 + (n - 1)5 ⇒ 78 = 3 + 5n - 5 ⇒ 78 = 5n - 2 ⇒ 5n = 78 + 2 ⇒ 5n = 80 ⇒ n = 16. Hence, 78 is 16th term of the A.P. (ii) The given A.P. is Here, first term = a = 18 and common difference = d = . Let -47 be nth term of the A.P., or a_n = -47 The nth term of A.P. is given by a_n = a + (n - 1)d Putting value of a, d and a_n in above equation we get, Hence, -47 is 27th term of the A.P.

Mathematics

Which term of the A.P. (i) 3, 8, 13, 18, ... is 78 ? (ii) is -47 ?

AP GP

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