Find the next three terms of the sequence below.

2, 4, 8, 16,...

My answers: 32, 64, 128

Find the next three terms of the sequence below.

2, -6, 18, -54,...

My answers: 162, -486, 1458

An = 2^n

Yes, correct

A1 = 2
r = -3
yes, correct

To find the next three terms of a sequence, we first need to identify the pattern or rule that governs the sequence. Let's analyze each sequence separately.

Sequence 1: 2, 4, 8, 16,...

If we look closely, we can see that each term is obtained by multiplying the previous term by 2. So, starting from 2, we multiply each term by 2 to get the next term:

2 x 2 = 4
4 x 2 = 8
8 x 2 = 16

Therefore, the next three terms of this sequence are:

16 x 2 = 32
32 x 2 = 64
64 x 2 = 128

So your answers of 32, 64, and 128 are correct.

Sequence 2: 2, -6, 18, -54,...

In this sequence, if we closely observe, each term is obtained by multiplying the previous term by -3. So, starting from 2, we multiply each term by -3 to get the next term:

2 x -3 = -6
-6 x -3 = 18
18 x -3 = -54

Therefore, the next three terms of this sequence are:

-54 x -3 = 162
162 x -3 = -486
-486 x -3 = 1458

So your answers of 162, -486, and 1458 are correct.

By identifying the pattern within each sequence, we can determine the next terms accurately.