Question

Find the first six terms of the sequence.

a1 = -1, an = 2 • an-1

Answer 1

The prompt says that the value at n is equal to 2 times the previous value.
-1, -2, -4, -8, -16, -32

Answer 2

The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32

Explanation:

The sequence is:

`a_1=-1\\a_n=2*a_(n-1)`

So, for finding the first six terms of the sequence, we need to replace n by the numbers 1 to 6 and we get:

`a_1=-1\\a_2=2*a_(2-1) =2*a_1\\a_3=2*a_(3-1) =2*a_2\\a_4=2*a_(4-1) =2*a_3\\a_5=2*a_(5-1) =2*a_4\\a_6=2*a_(6-1) =2*a_5\\`

That means that the term n is 2 times the last term. Then, replacing the values of
`a_1, a_2, a_3, a_4` and
`a_5`, we get:

`a_1=-1\\a_2=2*(-1)=-2\\a_3=2*(-2)=-4\\a_4=2*(-4)=-8\\a_5=2*(-8)=-16\\a_6=2*(-16)=-32\\`

So, The first six terms of the sequence are: -1, -2, -4, -8, -16 and -32