Question

Find the 31st term of an Ap whose 11th term is 38 and 164h term is 73.​

Answer 1

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

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

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• 11th term is 38.

• 16th term is 73

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

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• The 31st term of the same AP

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

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$\dashrightarrow\sf a_{11}$  = 38

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$\sf \dashrightarrow a_{16}$  = 73

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

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$\purple\longrightarrow$ an = a + (n − 1) d

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$\sf \longmapsto$ a11 = a + (11 − 1) d

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$\sf \longmapsto$ 38 = a + 10d ----------(1)

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$\underline{\bold{\texttt{Similarly,}}}$

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$\sf \longmapsto$ a16 = a + (16 − 1) d

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$\sf \longmapsto$ 73 = a + 15d ----------(2)

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$\underline{\bold{\texttt{Subtracting (1) from (2), we obtain}}}$

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$\sf \longmapsto 35 = 5d$

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$\sf \longmapsto$ d = 7

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$\underline{\bold{\texttt{From equation (1),}}}$

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$\sf \longmapsto$ 38 = a + 10 × (7)

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$\sf \longmapsto$ 38 − 70 = a

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$\sf \longmapsto a = -32$

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$\longmapsto$ a31 = a + (31 − 1)d

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$\sf \longmapsto$ a31= − 32 + 30 (7)

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$\sf \longmapsto a_{31}$ = − 32 + 210

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$\sf \longmapsto a_{31} = 178$

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Hence, 31st term is 178.

$\rule{200}5$

Answer 2

Answer:

answer is 178

Step-by-step explanation:

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