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.