Question

If a_(1)=3 and a_(n)=-2a_(n-1) then find the value of a_(5).

Answer 1

To find the value of a_5, we can use the given recursive formula a_n = -2a_n-1. By substituting the values step-by-step, we find that a_5 is equal to 48.

Step-by-step explanation:

To find the value of a5, we need to use the given recursive formula. We start with a1 = 3 and use the formula an = -2an-1 to find the subsequent terms.

Using the formula, we can find the values of a2, a3, a4, and a5 as follows:

1. a2 = -2a1 = -2(3) = -6
2. a3 = -2a2 = -2(-6) = 12
3. a4 = -2a3 = -2(12) = -24
4. a5 = -2a4 = -2(-24) = 48

Therefore, a5 = 48.