Question

Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.) a[1]=5,a[k+1]=-a[k]
I know:
a[1] = 5, a[2] = -5, a[3] = 5, a[4] = -5, a[5] = 5

Answer 1

Basically you are multiplying by negative one each time... so your sequence will look like:
\[a _{n}=(-1)^{n+1}\times5\]