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Alja [10]
2 years ago
14

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?

Mathematics
1 answer:
Soloha48 [4]2 years ago
8 0

<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

a_n=a(r)^{n-1}

where a is the first term and r is the common ratio.

The 11th term is given is

a_{11}=a(4)^{11-1}

48=a(4)^{10} ------- (1)

The 12th term is given by

192=a(4)^{11} ------- (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;

48=a(1048576)

Dividing both sides by 1048576, we get;

\frac{3}{65536}=a

Thus, the value of a is \frac{3}{65536}

<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 a_n=a(r)^{n-1}, we get;

a_{10}=\frac{3}{65536}(4)^{10-1}

a_{10}=\frac{3}{65536}(4)^{9}

a_{10}=\frac{3}{65536}(262144)

a_{10}=\frac{786432}{65536}

a_{10}=12

Thus, the 10th term of the sequence is 12.

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