Question

In an A.P. the 10 term is 46, sum of the 5 and 7 term is 52. Find the A.P.​

Answer 1

As we're provided in the question that, the 10th term of AP is 46. and the sum of 5th and 7th term is 52.

Then, We have to calculate the AP.

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$\bigstar\:{\boldsymbol{\underline{So,~ Let's~ head~ to~ the~ Question~ now~:}}}$

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✇ 10 term of AP (a₁₀) = 46

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⤏a + 9d = 46

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⤏ $\sf \red{a = 46 - 9d}$ -------eqⁿ (1)

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✇ Sum of 5th and 7th term (a₅ + a₇) = 52

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⤏ (a + 4d) + (a + 6d) = 52

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⤏ $\sf \red{2a + 10d = 52}$ -------eqⁿ (2)

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By Putting eqⁿ (1) in eqⁿ (2) :

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⤏ 2(46 - 9d) + 10d = 56

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⤏ 96 - 18d + 10d = 56

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⤏ 96 - 8d = 56

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⤏ - 8d = 56 - 96

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⤏ - 8d = - 40

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⤏ $\sf \purple{d = 40}$ (Common Difference)

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Now, By Putting value of d in eqⁿ (1) :

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⠀⠀⤏ a = 46 - 9(5)

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⠀⠀⤏ a = 46 - 45

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⤏ $\sf \purple{a = 1}$ (First term)

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$\therefore$ Hence, Our required terms of AP will be :

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General formula of AP :: a , a + d , a + 2d , a + 3d,...

⠀⠀》》${\sf{\pmb{\purple{1\:,\: 6 \:,\: 11 \:, \:16\: ,....,\: 5n - 4}}}}$《《

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☆ Some important formulas related to Arithmetic Progression ::

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• nth term of AP = a + (n - 1)d

• Sum of n terms of AP = n/2[2a + (n − 1) × d]