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Method and examples
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Geometric Progression |
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Problem 5 of 23 |
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5. For geometric progression f( ) = , f( ) = , then find n such that f(n) = .
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Solution
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Solution provided by AtoZmath.com
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This is demo example. Please click on Find button and solution will be displayed in Solution tab (step by step)
| Geometric Progression |
5. For geometric progression f( 1 ) = 2 , f( 4 ) = 54 , then find n such that f(n) = 18 .
We know that, `a_n = a × r^(n-1)`
Here `a_1 = 2`
`=> a × r^(1 - 1) = 2`
`=> a × r^0 = 2`
`=> a = 2 ->(1)`
`a_4 = 54`
`=> a × r^(4 - 1) = 54`
`=> a × r^3 = 54 ->(2)`
Solving `(1)` and `(2)`, we get `a = 2` and `r = 3`
Let n be the term such that `f(n) = 18`
We know that, `a_n = a × r^(n-1)`
`=> 2 × 3^(n-1) = 18`
`=> 3^(n-1) = 9`
`=> 3^(n-1) = 3^2`
`=> n - 1 = 2`
`=> n = 2 + 1`
`=> n = 3`
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