what are the next three terms in the sequence?
5,-9,19,-37,75, ___, ____, ____
for each step, multiply by -2 and add 1.
Thank you!
To find the next three terms in the sequence, we need to observe the pattern or rule behind the given terms. Let's analyze the differences between consecutive terms:
First term: 5
Second term: -9
The difference between the second term and the first term is -14 (obtained by subtracting the first term from the second term). Notice that the difference alternates between negative and positive values.
Second term: -9
Third term: 19
The difference between the third term and the second term is 28. Again, we see that the difference alternates between negative and positive values.
Third term: 19
Fourth term: -37
The difference between the fourth term and the third term is -56.
Based on this pattern, we can deduce that the differences alternate between subtracting 14 and adding 28. So, the next three differences in the sequence would be -14, 28, -14.
To find the next three terms in the sequence, we need to apply these differences to the last given term:
Last given term: 75
Next term: 75 + (-14) = 61
Following term: 61 + 28 = 89
Subsequent term: 89 + (-14) = 75
Therefore, the next three terms in the sequence are 61, 89, and 75.