Question

find 12th term of geometric progression whose 8th term is 192 and the common ratio is 2

Answer 1

$\boxed {\bold {a_n = a_1r^{n-1}}}$

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Given that the ratio is 2 and the 8th term is 192:

$a_8 = a_1r^7$

$192 = a_12^7$

$192 = 128a_1$

$a_1 = 192 \div 128 = 1.5$

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Therefore the geometry progression is :

$a_n = 1.5 \times 2^{n-1}$

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Find the 12th term:

$a_n = 1.5 \times 2^{n-1}$

$a_{12} = 1.5 \times 2^{12-1}$

$a_12 = 3072$

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Answer: 3072