Question

if 24th term is term the 10th term prove that 72nd term is term the 34th term

Answer 1

by finding the value of d ... here is the answer in the pic...

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• 24th term is term the 10th term

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$\red{\underline \bold{To \: Prove:}}$

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• 72nd term is term the 34th term

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{We know that :}}}$

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$\purple\longrightarrow$ $\bf a_n = a + (n - 1)d$

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• $\rm a_n$ = nth term

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• a = First term

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• n = Number of term

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• d = Common difference

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$\underline{\bold{\texttt{24th term :}}}$

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$\bf \dag \: \: \: a + (24 - 1)d$ -----(1)

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$\underline{\bold{\texttt{10th term :}}}$

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$\bf \dag \: \: \: a + (10 - 1)d$ -----(2)

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$\purple{\bold{Given \: that \: (1) \: = \: (2)}}$

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$\sf \longmapsto a + 23d = a + 9d$

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$\sf \longmapsto 23d - 9d = 0$

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$\sf \longmapsto 14d = 0$

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$\bf \dashrightarrow d = 0$

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$\underline{\bold{\texttt{72nd term :}}}$

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$\sf \longmapsto a + (72 - 1)0$

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$\sf \longmapsto a + (71)\times 0$

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$\bf \dag \: \: \: a$ ------(3)

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$\underline{\bold{\texttt{34th term :}}}$

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$\sf \longmapsto a + (34 - 1)0$

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$\sf \longmapsto a + (33) \times 0$

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$\bf \dag \: \: \: a$ -------(4)

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$\purple{\bold{We \: got \: (3) \: =\: (4)}}$

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Hence 72nd term is 34th term.

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$\red{\bold{Proved }}$

$\rule{200}5$