Q41Multiple correct2 Marks20 Nov 2022Consider a sequence (1,2,3,4,5,6,…)(1,2,3,4,5,6,\ldots)(1,2,3,4,5,6,…), that is, an=na_n=nan=n for all n∈Nn\in\mathbb{N}n∈N. Which of the following sequences are subsequences of {an}\{a_n\}{an}?A(1,3,1,3,…)(1,3,1,3,\ldots)(1,3,1,3,…), that is, bn=1b_n=1bn=1 if nnn is odd and bn=3b_n=3bn=3 if nnn is even.B(1,3,5,7,…)(1,3,5,7,\ldots)(1,3,5,7,…), that is, bn=2n−1b_n=2n-1bn=2n−1 for all n∈Nn\in\mathbb{N}n∈N.C(1,1,2,2,3,3,…)(1,1,2,2,3,3,\ldots)(1,1,2,2,3,3,…), that is, bn=n+12b_n=\frac{n+1}{2}bn=2n+1 if nnn is odd and bn=n2b_n=\frac{n}{2}bn=2n if nnn is even.D(1,8,27,64,…)(1,8,27,64,\ldots)(1,8,27,64,…), that is, bn=n3b_n=n^3bn=n3 for all n∈Nn\in\mathbb{N}n∈N.
