I need help on this question...
"Make a conjecture about the next item in the sequence.
1,-2,-5,-8,-11,?
Please help...
looks like you are subtracting 3 from each term to get the next one,
an arithmetic sequence.
1, –8, –17, –26, –35
To find the pattern in the given sequence, we can observe that each term is decreasing by 3.
1 - 3 = -2
-2 - 3 = -5
-5 - 3 = -8
-8 - 3 = -11
From this pattern, we can deduce that the next term would be obtained by subtracting 3 from the previous term.
So, the next number in the sequence would be -11 - 3 = -14.
Therefore, the conjecture for the next item in the sequence is -14.
To find a pattern and make a conjecture about the next item in the sequence, let's look at the differences between consecutive terms:
1 - (-2) = 3
-2 - (-5) = 3
-5 - (-8) = 3
-8 - (-11) = 3
Looking at the differences, we can observe that they are all equal to 3. So, we can assume that the next difference will also be 3.
To determine the next term, we add 3 to the last term in the sequence:
-11 + 3 = -8
Therefore, we can make a conjecture that the next item in the sequence is -8.
You can solve similar problems by identifying the pattern in the given sequence, focusing on the differences or ratios between the terms, and then using that pattern to determine the next term.