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<u>Given</u>:
The 11th term in a geometric sequence is 48.
The 12th term in the sequence is 192.
The common ratio is 4.
We need to determine the 10th term of the sequence.
<u>General term:</u>
The general term of the geometric sequence is given by
where a is the first term and r is the common ratio.
The 11th term is given is
------- (1)
The 12th term is given by
------- (2)
<u>Value of a:</u>
The value of a can be determined by solving any one of the two equations.
Hence, let us solve the equation (1) to determine the value of a.
Thus, we have;
Dividing both sides by 1048576, we get;
Thus, the value of a is
<u>Value of the 10th term:</u>
The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term , we get;
Thus, the 10th term of the sequence is 12.