What is the value of the fourth term in a geometric sequence for which a110 and r0.5?

To find the fourth term in a geometric sequence where the first term ( a_1 = a_{10} ) and the common ratio ( r = 0.5 ), we can use the formula for the ( n )-th term of a geometric sequence: ( a_n = a_1 \cdot r^{n-1} ). Since ( a_{10} = a_1 \cdot r^9 ), we can set ( a_1 \cdot (0.5)^9 = a_1 ). This implies ( (0.5)^9 = 1 ), which is not possible. Therefore, the sequence must start with ( a_1 = 0 ), making all terms including the fourth term equal to 0. Thus, the value of the fourth term is 0.