Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

Answer 1

The first term of this geom. sequence is obviously -2. We represent that by a=-2.
What multiplier gets us from -2 to +8?
What multiplier gets us from +8 to -32?
From -32 to +128?
If you do your math correctly, you'll find that the multiplier is the same.

Call this multiplier, also known as the "common ratio," r.

Can you now write a formula for the nth term of this geometric sequence, using the "a" and "r" values you've found here? If not, look u p "geometric sequence" on the 'Net; you'll quickly find the appropriate formula.

Answer 2

Table[ ( (-1)^n) 2^(2n-1), { n, 1, 6 } ] = { -2, 8, -32, 128, -512, 2048 }