The 11th term in a geometric sequence is 48 and the common ratio is 4. the 12th term is 192 and the 10th term is what?

If the 11th term in a geometric sequence is 48, the common ratio is 4, and the 12th term is 192, then the 10th term = 12

The nth term of a geometric sequence is:

11th term in a geometric sequence is 48 and the common ratio is 4

The 12th term of the geometric sequence is:

The 10th term will be given as:

The 10th term = 12

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Given:

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.

General term:

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)

Value of a:

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

Value of the 10th term:

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.

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step-by-step explanation: