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Method and examples
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Arithmetic Progression |
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Problem 17 of 19 |
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17. For arithemetic progression, addition of three terms is and multiplication of end 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 |
17. For arithemetic progression, addition of three terms is 51 and multiplication of end terms is 273 , then find that numbers
Let the terms are `a-d, a, a+d`
Addition of this terms is `51`
`=> (a-d) + a + (a+d) = 51`
`=> 3 a = 51`
`=> a = 51/3 = 17`
Multiplication of last 2 terms is `273`
`=> (a-d)(a+d) = 273`
`=> a^2 - d^2 = 273`
`=> d^2 = a^2 - 273`
`=> d^2 = (17)^2 - 273`
`=> d^2 = 289 - 273`
`=> d^2 = 16`
`=> d = +- 4`
`d = +4 =>` Required terms : `17 - 4, 17, 17 + 4 => 13, 17, 21`
`d = -4 =>` Required terms : `17-(-4), 17, 17-4 => 21, 17, 13`
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