Subjects algebra

Arithmetic Sequence 6A121E

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1. The problem is to find the next term in the sequence: 29, 17, 5, ... 2. Observe the pattern by finding the difference between consecutive terms: $$17 - 29 = -12$$ $$5 - 17 = -12$$ 3. The difference between terms is constant and equals $-12$, so this is an arithmetic sequence with common difference $d = -12$. 4. Use the formula for the $n$th term of an arithmetic sequence: $$a_n = a_1 + (n-1)d$$ where $a_1 = 29$ and $d = -12$. 5. To find the 4th term ($a_4$): $$a_4 = 29 + (4-1)(-12) = 29 + 3 \times (-12) = 29 - 36 = -7$$ 6. Therefore, the next term in the sequence is $-7$.