Question

Find the 23 rd term of an AP whose first two terms are -2 and 5.​

Answer 1

Answer:

$a = - 2 \\ d = 5 - ( - 2) = 5 + 2 = 7 \\ T_{23} = \: ?? \\ \\ T_{n} = a + (n - 1)d \\ T_{23} = - 2 + (23 - 1)7 \\ T_{23} = - 2 + (22)7 \\ T_{23} = - 2 + 154 \\ T_{23} = \underline{ \underline{ \large \bf 152}}$

Answer 2

Given :- ⠀

• $\sf -2 \: and \: 5 \: are \: the \: first \: 2\: terms \: of \: an \: AP$

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To find :-

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• $\sf 23rd \: term \: of \: the \: AP = ??$

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Solution :-

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$\bigstar\:{\underline{\sf We \:know \:that \::}}$

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$\star\:{\boxed{\sf{\pink{t_n = a + ( n -1 ) d }}}}$

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Where ;

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● a = 1st term

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● n = no. of term

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● d = common difference

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Here ;

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◉ a = -2

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◉ n = 23

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◉ d = 2nd term - 1st term = 5 - ( -2 ) = 5 + 2 = 7

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$\sf : \implies a_{23} = -2 + ( 23 - 1 ) 7$

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$\sf : \implies a_{23} = -2 + 22 \times 7$

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$\sf : \implies a_{23} = -2 + 154$

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$\sf : \implies a_{23} = 152$

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$: \implies{\underline{\boxed{\frak{\purple{23rd \: term = \: 152 }}}}}\;\bigstar$

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$\therefore\:{\underline{\sf{23rd \; term \; of \;the \: A.P. \; is \; \bf{ 152 }.}}}$

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