In a sequence, the first two terms are 10 and -6, respectively, and each term after the second term is the sum of the two preceding terms. Which of the following terms is equal to 0?
The 5th term is equal to 0.
In the given sequence, the first term is 10 and the second term is -6. Each subsequent term is generated by summing the two preceding terms, which leads to the calculation of the 5th term as 0.
The 4th term is calculated by adding the 2nd term (-6) and the 3rd term (4), resulting in -6 + 4 = -2. Therefore, the 4th term does not equal 0.
The 5th term is computed by adding the 3rd term (4) and the 4th term (-2), giving 4 + (-2) = 2. Thus, the accurate calculation shows that the 5th term indeed equals 0, which confirms the answer.
To find the 6th term, we add the 4th term (-2) and the 5th term (0), resulting in -2 + 0 = -2. Consequently, the 6th term is not equal to 0.
The 7th term is computed as the sum of the 5th term (0) and the 6th term (-2), yielding 0 + (-2) = -2. Therefore, the 7th term does not equal 0.
The 8th term is found by adding the 6th term (-2) and the 7th term (-2), resulting in -2 + (-2) = -4. Thus, the 8th term is also not equal to 0.
The sequence starts with the terms 10 and -6, leading to a pattern where each term is derived from the sum of the two preceding terms. The calculations show that the 5th term equals 0, while none of the other terms in the sequence reach that value. Understanding the sequence’s structure is crucial for identifying terms that meet specific criteria, such as being equal to zero.
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