Q. 24.0( 2 Votes )

Find the indicated terms in each of the sequences whose nth terms are given by

(i) (ii) an = (-1)n 2n + 3 (n + 1); a5, a8

(iii) an = 2n2 – 3n + 1; a5, a7 (iv) an = (-1)n (1 – n + n2); a5, a8

Answer :

(i) Here, an =


For n = 7, a7 = = =


For n = 9, a9 = = =


(ii) Here, an = (-1)n 2n + 3 (n + 1)


For n = 5, a5 = (-1)5 25 + 3 (5 + 1) = (-1) 28 (6) = -6 (256) = -1536


For n = 8, a8 = (-1)8 28 + 3 (8 + 1) = (1) 211 (9) = 9 (2048)


= 18432


(iii) Here, an = 2n2 – 3n + 1


For n = 5, a5 = 2(5)2 – 3(5) + 1 = 2(25) – 15 + 1 = 50 – 15 + 1


= 36


For n = 7, a7 = 2(7)2 – 3(7) + 1 = 2(49) – 15 + 1 = 98 – 21 + 1


= 78


(iv) Here, an = (-1)n (1 – n + n2)


For n = 5, a5 = (-1)5 (1 – 5 + 52) = (-1) (1 – 5 + 25) = (-1) (21)


= -21


For n = 8, a5 = (-1)8 (1 – 8 + 82) = (1) (1 – 8 + 64) = (1) (57)


= 57


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