(an)=(2n-1) is a sequence.

(an+1) and (a2n) are subsequences of (an).

Is the following statement true?

"Sum of the subsequences is also a subsequence."

According to me this is wrong. According to the book true.

When we put n+1 in place of n we get 2n+1

When we put 2n in place of n we get 4n-1

If we sum 2n+1+4n-1=6n.So the sum is not a subsequence.