The next term of a sequence is made by adding the previous two terms.
Which of these sequences follow this rule?
-9 2 -7 -5 -12 -3 5 -2 3 1
0 -3 -3 0 -3. -1 -1 -2 -3 1
The first and second sequences follow the rule.
wtf
I'm sorry, did my response not make sense to you? Perhaps I can explain it better.
The rule states that the next term in the sequence is found by adding the previous two terms.
In the first sequence (-9, 2, -7, -5, -12), you can see that 2 is obtained by adding -9 and -7, and -7 is obtained by adding 2 and -9. This continues through the rest of the sequence, so it follows the rule.
In the second sequence (-3, 5, -2, 3, 1), you can see that 5 is not obtained by adding the previous two terms, since there is no negative term before it. Therefore, this sequence does not follow the rule.
In the third sequence (0, -3, -3, 0, -3), you can see that each term is the same as the term two terms before it, so it does not follow the rule either.
Finally, in the fourth sequence (-1, -1, -2, -3, 1), you can see that each term is obtained by adding the previous two terms, so it follows the rule.
To determine whether a sequence follows the rule of adding the previous two terms, we need to check if each term is the sum of the previous two terms.
Let's start by examining the first sequence: -9 2 -7 -5 -12.
To identify whether a term is obtained by adding the two preceding terms, we can verify this property for each term in the sequence:
-9 = 2 + (-7) [First term = sum of the second and third term - True]
2 = -7 + (-5) [Second term = sum of the third and fourth term - True]
-7 ≠ -5 + (-12) [Third term ≠ sum of the fourth and fifth term - False]
-5 ≠ -12 + (previous term before -12) [Fourth term ≠ sum of the fifth term and the previous term - False]
-12 ≠ (previous term before -12) + (previous term before the previous term before -12) [Fifth term ≠ sum of the previous term before -12 and previous term before the previous term before -12 - False]
Based on the first sequence, it seems that it does not follow the rule of adding the previous two terms since the third term onwards does not satisfy the given property.
Now let's examine the second sequence: -3 5 -2 3 1.
-3 = 5 + (-2) [First term = sum of the second and third term - True]
5 = -2 + 3 [Second term = sum of the third and fourth term - True]
-2 = 3 + (previous term before 3) [Third term = sum of the fourth term and the previous term - True]
3 = (previous term before 3) + (previous term before the previous term before 3) [Fourth term = sum of the previous term before 3 and the previous term before the previous term - True]
1 ≠ (previous term before 1) + (previous term before the previous term before 1) [Fifth term ≠ sum of the previous term before 1 and the previous term before the previous term - False]
Based on the second sequence, it also does not fulfill the rule from the third term onwards.
Finally, let's examine the third sequence: 0 -3 -3 0 -3.
0 = -3 + (-3) [First term = sum of the second and third term - True]
-3 ≠ -3 + 0 [Second term ≠ sum of the third term and the previous term - False]
-3 ≠ 0 + (-3) [Third term ≠ sum of the fourth term and the previous term - False]
0 ≠ (-3) + (-3) [Fourth term ≠ sum of the previous term before 0 and the previous term before the previous term - False]
-3 ≠ (-3) + (previous term before -3) [Fifth term ≠ sum of the previous term before -3 and the previous term before the previous term - False]
Based on the third sequence, it also does not satisfy the rule for any term.
Neither of the given sequences follow the rule of adding the previous two terms.