Question

The 21st term of the given sequence -11,-15,-19

Answer 1

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$\sf \red\star\pmb {Understanding \: \: Question }$

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Here a sequence is given and we have to find the 21st term of the given sequence. But first we have to find the nth term for the sequence and then substitute the values and get out the required answer.

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$\sf \red \star \pmb{Formula \: \: used }$

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$\qquad \dashrightarrow \sf{ a_{n} = a + (n - 1)d}$

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Where~

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• a donates the first number of the sequence
• n donates the term ( eg :- 21st term )
• d donates the difference between the first and the second number .

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$\red\star \sf \pmb{According \: \: to \: \: the \: \: question}$

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• a = -11
• d = -11 - (-15) = -11 + 15 = 4

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$\sf{ {21}^{th} \: term \: of \: the \: sequence \downarrow}$

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$\qquad \bf \rightarrow{ a_{n} = - 11 + (n - 1)4}$

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$\qquad \rightarrow \sf{ a_{n} = - 11 + 4n - 4}$

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$\qquad \rightarrow \sf{ a_{n} = - 11 - 4 + 4n }$

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$\qquad \rightarrow \sf{ a_{n} = - 15 + 4n }$

$\begin{gathered}{ \underline{ \red{ \boxed{ \tt{Therefore, the \: {n}^{th} \: term \: of \: the \: sequence \: is \: a_{n} = -15 + 4n}}}}} \end{gathered}$

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$\red \star \sf \pmb{Finding \: \: the \: \: {21}^{th} \: \: term \: of \: the \: sequence }$

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$\qquad \rightarrow \sf{ - 15+ 4n}$

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$\qquad \rightarrow{ - 15 + 4 \times 21}$

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$\qquad \rightarrow \sf{ - 15 + 84}$

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$\qquad\rightarrow{ 69}$

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$\begin{gathered}{ \underline{ \red{ \boxed{ \tt{Therefore, \: the \: {21}^{th} \: term \: of \: the \: sequence \: is \: 69}}}}} \end{gathered}$

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