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Method and examples
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Arithmetic Progression |
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Problem 19 of 19 |
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19. For arithemetic progression, addition of four terms is and addition of multiplication of end terms and multiplication of middle 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 |
19. For arithemetic progression, addition of four terms is 4 and addition of multiplication of end terms and multiplication of middle terms is -38 , then find that numbers
Let the terms are `a-3d, a-d, a+d, a+3d`
Addition of this terms is `4`
`=> (a-3d) + (a-d) + (a+d) + (a+3d) = 4`
`=> 4 a = 4`
`=> a = 4/4 = 1`
Addition of multiplication of last 2 terms and middle 2 terms is `-38`
`=> (a-3d) (a+3d) + (a-d) (a+d) = -38`
`=> (a^2 - 9d^2) + (a^2 - d^2) = -38`
`=> 2a^2 - 10d^2 = -38`
`=> 2(1)^2 - 10d^2 = -38`
`=> 2 - 10d^2 = -38`
`=> 10d^2 = 40`
`=> d^2 = 4`
`=> d = +- 2`
`d = +2 =>` Required terms : `1-3(2), 1-2, 1+2, 1+3(2) => -5, -1, 3, 7`
`d = -2 =>` Required terms : `1-3(-2), 1-(-2), 1-2, 1-3(2) => 7, 3, -1, -5`
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