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  • The sum of the 5thand the 7thterms of an AP is 52 and the 10th term is 46. Find the AP.

The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

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\\$Given a\textsubscript{5} + a\textsubscript{7}$=52 \\ a\textsubscript{5}=a+4d a\textsubscript{7}= a + 6d (using a\textsubscript{n} = a + (n-1).d) \\ $Given a\textsubscript{10}$= 46 \\ \therefore a+9d=46 $ \ldots $ .(1) \\ a + 4d + a + 6d = 52\\ 2a + 10d = 52\\ $Dividing both side by 2$\\ a + 5d = 26 $ \ldots $ (2)\\ a + 9d =\_ 46 \\ \\ -4d = - 20\\ d=\frac{-20}{-4} \\ d = 5 \\ $Put d = 5 in equation (1) we get$\\ a + 5 \times (5) = 26\\ a + 25 = 26\\ a = 26 - 25\\ a = 1\\ a\textsubscript{1} = a = 1\\ a\textsubscript{2} = a + d \\ = 1 + 5\\ = 6\\ a\textsubscript{3} = a + 2d \\ = 1 + 2 \times (5) \\ = 1 + 10 \\ = 11\\

Hence the AP is 1, 6, 11....

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