Answer to Question #155602 in Calculus for prince

Question

Write a formula for the an in each of the following sequences _{an} ^∞ _n=1 given by

(i) 2, 1, 4, 3, 6, 5, 8, 7, . . .

(ii) 1, 3, 6, 10, 15, . . .

(iii) 1, −4, 9, −16, 25, −36, . . . Which ones among these are the subsequence of {n} ^∞ _n=1?

Answer 1

Formulas for a given sequences:

1) $a_n=a_{n-1}+1+2(-1)^{n-1}$ , $a_{1}=2$

and is not a subsequence of ${n}_{n=1}^{\infty}$ cause have different order of members

2) $a_n=a_{n-1}+n$ , $a_{1}=1$

and is a subsequence of ${n}_{n=1}^{\infty}$

3) $a_n=(-1)^{n-1}n^2$

and is not subsequence of ${n}_{n=1}^{\infty}$ cause have other members and order of them