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Method and examples
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Arithmetic Progression |
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Problem 14 of 19 |
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14. For arithemetic progression addition of three terms is and addition of their squres 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 |
14. For arithemetic progression addition of three terms is 15 and addition of their squres is 83 , then find that numbers
Let the terms are `a-d, a, a+d`
Addition of this terms is `15`
`=> (a-d) + a + (a+d) = 15`
`=> 3 a = 15`
`=> a = 15/3 = 5`
Addition of their square is `83`
`=> (a-d)^2 + a^2 + (a+d)^2 = 83`
`=> a^2 - 2ad + d^2 + a^2 + a^2 + 2ad + d^2 = 83`
`=> 3a^2 + 2d^2 = 83`
`=> 3(5)^2 + 2d^2 = 83`
`=> 2d^2 = 8`
`=> d^2 = 4`
`=> d = +- 2`
`d = +2 =>` Required terms : `5 - 2, 5, 5 + 2 => 3, 5, 7`
`d = -2 =>` Required terms : `5-(-2), 5, 5-2 => 7, 5, 3`
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