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Method and examples
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Geometric Progression |
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Problem 4 of 23 |
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4. For geometric progression f( ) = , f( ) = then find f( ) and S( ).
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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 |
4. For geometric progression f( 1 ) = 2 , f( 4 ) = 54 then find f( 3 ) and S( 3 ).
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`
We know that, `a_n = a × r^(n-1)`
`a_3 = 2 × 3^(3 - 1)`
`= 2 × 9`
`= 18`
We know that, `S_n = a * (r^n - 1)/(r - 1)`
`:. S_3 = 2 × (3^3 - 1)/(3 - 1)`
`=> S_3 = 2 × (27 - 1)/2`
`=> S_3 = 2 × 26/2`
`=> S_3 = 26`
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