11. The twelfth term, t_(12) , in the sequence 43,37,31,25,ldots A. -72 B. -23 C. -6 D. 12

To find the twelfth term in the sequence, we need to determine the pattern or rule that the sequence follows. Let's examine the given terms:<br /><br />- The first term is 43.<br />- The second term is 37.<br />- The third term is 31.<br />- The fourth term is 25.<br /><br />We can see that each term is decreasing by 6 from the previous term. This is a common difference, indicating that the sequence is an arithmetic sequence.<br /><br />The general formula for the nth term of an arithmetic sequence is given by:<br /><br />\[ t_n = a + (n - 1)d \]<br /><br />where:<br />- \( a \) is the first term,<br />- \( d \) is the common difference,<br />- \( n \) is the term number.<br /><br />For this sequence:<br />- The first term \( a = 43 \),<br />- The common difference \( d = -6 \).<br /><br />We need to find the 12th term (\( t_{12} \)):<br /><br />\[ t_{12} = 43 + (12 - 1)(-6) \]<br />\[ t_{12} = 43 + 11(-6) \]<br />\[ t_{12} = 43 - 66 \]<br />\[ t_{12} = -23 \]<br /><br />Therefore, the twelfth term in the sequence is:<br /><br />B. \(-23\)