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Method and examples
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Arithmetic Progression |
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Problem 2 of 19 |
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2. For arithemetic 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)
| Arithmetic Progression |
2. For arithemetic progression f( 5 ) = 56 , f( 8 ) = 86 then find f( 10 ) and S( 10 ).
We know that, `f(n) = a + (n - 1)d`
`f(5) = 56`
`=> a + (5 - 1)d = 56`
`=> a + 4d = 56 ->(1)`
`f(8) = 86`
`=> a + (8 - 1)d = 86`
`=> a + 7d = 86 ->(2)`
Solving `(1)` and `(2)`, we get `a = 16` and `d = 10`
We know that, `f(n) = a + (n - 1)d`
`f(10) = 16 + (10 - 1)(10)`
`= 16 + (90)`
`= 106`
We know that, `S_n = n/2 [2a + (n - 1)d]`
`:. S_10 = 10/2 * [2(16) + (10 - 1)(10)]`
`= 5 * [32 + (90)]`
`= 5 * [122]`
`= 610`
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