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Question Number 156495 by chusrang last updated on 11/Oct/21

1. Write the first three terms of each of the following sequences: (a) a_n = (3^n /(2^n + 1)) (b) a_n = (−1)^(n−1) n^3

$$\mathrm{1}.\:\mathrm{Write}\:\mathrm{the}\:\mathrm{first}\:\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequences}:\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{a}_{{n}} \:=\:\frac{\mathrm{3}^{{n}} }{\mathrm{2}^{{n}} \:+\:\mathrm{1}}\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{a}_{{n}} \:=\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {n}^{\mathrm{3}} \\ $$

Answered by Rasheed.Sindhi last updated on 11/Oct/21

(a) (3^1 /(2^1 +1)),(3^2 /(2^2 +1)),(3^3 /(2^3 +1)) (3/(2+1)),(9/(4+1)),((27)/(8+1)) (3/3),(9/5),((27)/9) 1,(9/5),3 (b) (−1)^(1−1) (1)^3 ,(−1)^(2−1) (2)^3 ,(−1)^(3−1) (3)^3 (−1)^0 (1), (−1)(8),(−1)^2 (27) 1, −8, 27

$$\left(\mathrm{a}\right)\:\frac{\mathrm{3}^{\mathrm{1}} }{\mathrm{2}^{\mathrm{1}} +\mathrm{1}},\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} +\mathrm{1}},\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{2}^{\mathrm{3}} +\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{3}}{\mathrm{2}+\mathrm{1}},\frac{\mathrm{9}}{\mathrm{4}+\mathrm{1}},\frac{\mathrm{27}}{\mathrm{8}+\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{3}}{\mathrm{3}},\frac{\mathrm{9}}{\mathrm{5}},\frac{\mathrm{27}}{\mathrm{9}} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1},\frac{\mathrm{9}}{\mathrm{5}},\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\left(−\mathrm{1}\right)^{\mathrm{1}−\mathrm{1}} \left(\mathrm{1}\right)^{\mathrm{3}} ,\left(−\mathrm{1}\right)^{\mathrm{2}−\mathrm{1}} \left(\mathrm{2}\right)^{\mathrm{3}} ,\left(−\mathrm{1}\right)^{\mathrm{3}−\mathrm{1}} \left(\mathrm{3}\right)^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\left(−\mathrm{1}\right)^{\mathrm{0}} \left(\mathrm{1}\right),\:\left(−\mathrm{1}\right)\left(\mathrm{8}\right),\left(−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{27}\right) \\ $$$$\:\:\:\:\:\:\mathrm{1},\:−\mathrm{8},\:\mathrm{27} \\ $$

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