Question

Find the third fourth and fifth terms of the sequence defined by a1=1, a2=3, and a n =(-1)n a n-2 for n>3

Answer 1

We have been given that

$a_1=1\\ a_2=3\\ a_ n =(-1)^n a _{n-2} \text{ for } n>3$

In order to find the third term, we substitute n=3

$a_ 3 =(-1)^3a _{(3-2)}\\ \\ a_ 3 =(-1)^3 a _{1}$

Substituting the given value of $a_1$

$a_ 3 =(-1)^3 \times 1\\ \\ a_3=-1\times 1\\ \\ a_3=-1$

Similarly, we can find the fourth term by plugging n=4

$a_ 4 =(-1)^4a _{(4-2)}\\ \\ a_ 4 =(-1)^4 a _{2}\\ \\ a_4= 1\times 3\\ \\ a_4=3$

Therefore, the third term is -1

And the fourth term is 3