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Method and examples
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Arithmetic Progression |
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Problem 8 of 19 |
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8. For arithemetic progression addition of first terms is and addition of first terms is , then find addition of first terms.
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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 |
8. For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms.
We know that, `S_n = n/2 [2a + (n - 1)d]`
`S_17 = 17/2 * [2a + (17 - 1)d] = 24`
`=> 17/2 * [2a + 16d] = 24`
`=> 2a + 16 d = 2.8235 ->(1)`
We know that, `S_n = n/2 [2a + (n - 1)d]`
`S_24 = 24/2 * [2a + (24 - 1)d] = 17`
`=> 24/2 * [a + 23d] = 17`
`=> 2a + 23d = 1.4167 ->(2)`
Solving `7 d = -1.4069`
`=> d = -0.201`
From `(1) => 2a + 16d = 2.8235`
`=> 2a = 2.8235 - 16d`
`=> 2a = 2.8235 - 16 × -0.201`
`=> 2a = 2.8235 - -3.2157`
`=> 2a = 6.0392`
`=> a = 3.0196`
We know that, `S_n = n/2 [2a + (n - 1)d]`
`:. S_41 = 41/2 * [2(3.0196) + (41 - 1)(-0.201)]`
`= 41/2 * [6.0392 + (-8.0392)]`
`= 41/2 × -2`
`= -41`
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