Question

$\small\tt{Find\:the\:20^{th}term\:of\:an}\\{\small\tt{ap\:13\:,\:8,\:3\ \textless \ br /\ \textgreater \ }}$​

Answer 1

Answer:

Explanation: a=13 , d= 8-13 = -5

An= a+(n-1)d

= 13+(n-1)(-5)

= 13+(-5n+5)

= 13-5n+5

= -5n+18

Answer 2

$\small\bf\purple{\underline{\boxed{Question}}}$

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$\small\tt{Find\:the\:20^{th}term\:of\:an}\\{\small\tt{ap\:13\:,\:8,\:3</p><p>}}$

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$\small\bf\purple{\underline{\boxed{Solution}}:-}$

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$\small\tt{a\:=\:13}$

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$\small\tt{d\:=\:d_{2}-{d_{1}}\:=\:8\:-\:3\:=\:-\:5}$

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$\small\tt{a_{n}}\:=\:20$

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$\small\bf\purple{\underline{\boxed{Formula}}}$

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$\small\tt{\underline{\boxed{a_{n}\:=\:a\:+\:(n-1)\:d}}}$

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$\small\tt{so\:,}$

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$\small\tt{a_{20}}\:=\:13\:+\:(20-1)\:(-5)$

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$\small\tt{a_{20}}\:=\:13\:+\:(19)\:(-5)$

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$\small\tt{a_{20}}\:=\:13\:+\:(19)\:(-5)$

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$\small\tt{a_{20}}\:=\:13\:+\:(-95)$

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$\small\tt{a_{20}}\:=\:13\:-\:95$

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$\small\tt\blue{\underline{\boxed{a_{20}\:=\:-82}}}$

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$\small\tt{so\:the\:20^{th}\:term\:of\:an\:ap\:is\:-82}$

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$\small\bf\purple{\underline{\boxed{Thanks}}}$