Question

please solve this ...........​

Answer 1

Question 1 :-

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State and prove Converse of Pythagoras theorem.

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Solution :-

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Refer to the above attachments !

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Question 2 :-

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In an A.P. 7 , 10 , 13 . . . . 184 , Find the 25th term from the last term.

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Solution :-

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Given :-

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$\sf \large{last \: term \: (l) = 184} \\ \\ \sf \large{ t_{1} = 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \large{ t_{2} = 10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \large{ t_{3} = 13} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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To find :-

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$\sf \large{The \: 25th \: from \: last = \purple{ t_{ 25} = \: ?}}$

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Formula used :-

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$\sf \large \green{ t_{n} = \: l \: + (n - 1) \: - d }$

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Answer :-

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Here we have to first find the value of d

So,

$\sf \large{ \leadsto \: d = t_{2} - t_{1} = 10 - 7 = \red{3} } \: \: \\ \sf \large{ \leadsto \: d = t_{3} - t_{2} = 13 - 10 = \red{3} }$

So we have found the value of d = 3

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Now using the formula ,

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$\longmapsto\sf \large \green{ t_{n} = l \: + (n - 1) - d } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \longmapsto \sf \large{ t_{ 25} = 184 + (25 - 1)( - 3)} \\ \longmapsto\sf \large{ t_{25} = 184 \: + 24( - 3) } \: \: \: \: \: \: \: \: \: \: \\ \longmapsto\sf \large{ t_{25} = 184 \: - 72 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \longmapsto\sf \large \red{{ t_{ 25} = 112}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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The 25th term of the A.P. from the last term is 112.

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( Here , the value of d is taken as negative because we are finding the difference from the last term )