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Method and examples
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Arithmetic Progression |
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Problem 18 of 19 |
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18. For arithemetic progression of four terms, addition of end terms is and multiplication of middle two terms is , then find that numbers
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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 |
18. For arithemetic progression of four terms, addition of end terms is 14 and multiplication of middle two terms is 45 , then find that numbers
Let the terms are `a-3d, a-d, a+d, a+3d`
Addition of last 2 term is `14`
`=> (a-3d) + (a+3d) = 14`
`=> 2a = 14`
`=> a = 14/2 = 7`
Now multiplication of middle two terms is `45`
`=> (a-d) (a+d) = 45`
`=> a^2 - d^2 = 45`
`=> d^2 = a^2 - 45`
`=> d^2 = 7^2 - 45`
`=> d^2 = 49 - 45`
`=> d^2 = 4`
`=> d = +- 2`
`d = +2 =>` Required terms : `7-3(2), 7-2, 7+2, 7+3(2) => 1, 5, 9, 13`
`d = -2 =>` Required terms : `7-3(-2), 7-(-2), 7-2, 7-3(2) => 13, 9, 5, 1`
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