Question

★ LaTeX Problem !!

1: How do I write number cancellation in LaTeX codè ?
refer attachment*

2: How can I write a topic/paragraph inside a box in LaTeX ?

★ Maths Problem !!

1: Find the $\sf{37^{th}}$ term of an A.P.
➪ 3 , 9 , 15 , 21 . . . . . . . . . . . . $\infty$

→ Request ←
Please provide answers in my previous questions !!
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Answer 1

Answer:

$\Large \underline\frak \red{\pmb{Question.1}}$

1: How do I write number cancellation in LaTeX codè ?

$\Large \underline\frak \red{\pmb{Answer}}$

For cancelling any number in latex we need to write \cancel before the number

• Check the 1st attachment Please...

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$\Large \underline \frak \red {\pmb{Question.2}}$

How can I write a topic/paragraph inside a box in LaTeX ?

$\Large\underline\frak\red{\pmb{Answer}}$

write a topic/paragraph inside a box in LaTeX we need to write \begin{gathered}\boxed{}\end{gathered}

• Starting = \begin{gathered}
• End = \end{gathered}
• Check the 2nd attachment Please.

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \sf \red{Answering \: By - LoveYouHindi }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$

\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \sf \red{Answering \: By - LoveYouHindi }\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}

$\begin{gathered}{\underline{\boxed{ \sf {\red{Answering \: By - LoveYouHindi}}}}}\end{gathered}$

\begin{gathered} {\underline{\boxed{ \sf {\red{Answering \: By - LoveYouHindi}}}}}\end{gathered}

• Here is the used latex côde...

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$\Large \underline \frak \red {\pmb{Question.3}}$

Find the 37th term of an A.P. 3 , 9 , 15 , 21 . . . . . . .

$\Large \underline\frak \red{\pmb{Answer}}$

$\underline{ \bf{Given}}$

• ➠ A.P - 3 , 9 , 15 , 21 . .

${\underline {\bf{To \: Find}}}$

• ➠ 37th term

$\underline{\bf{Using \: Formula }}$

$\circ{\underline {\boxed{ \sf{T_n=a+(n-1)d}}}}$

Where

• ➠ tn = nth term
• ➠ n = Number of Term
• ➠ a = First term
• ➠ d = Common deference

$\large \underline{\bf {Solution}}$

$\bigstar \: \underline \frak{\pmb{Here \: we \: know \: that:}}$

• ⇒ First Term = 3
• ⇒ Number of Term = 37

$\bigstar \: \underline\frak{\pmb{\: Finding \: Common \: Differences \: between \: terms}}$

$: \implies\sf{a_2-a_1}$

$: \implies \sf{9 - 3}$

$: \implies \sf{6}$

• ➛ Hence, The common difference between terms is 6.

$\bigstar \: \underline\frak{\pmb{Now \: Finding \: 37th \: Term}}$

$: \implies { \sf{T_n=a+(n-1)d}}$

• ⇒ Substituting the values

$\implies { \sf{T_{37}=3+(37-1) 6}}$

$\implies { \sf{T_{37}=3+(36 \times 6)}}$

$\implies { \sf{T_{37}=3 + 216}}$

$\implies { \sf{T_{37} = 219}}$

• ➛ Henceforth, The 37th term is 219.

$\underline{ \bf{{More \: Useful \: Formulae}}}$

★ Formula to find the numbers of term of an AP:

• $: \implies \sf{n= \bigg[ \dfrac{(l - a)}{d} \bigg]}$

★ Formula to find the tsum of first n terms of an AP:

• $: \implies\sf{S_n= \dfrac{n}{2} (a + l)}$

★ Formula to find the sum of squares of first n natural numbers of an AP:

• $: \implies \sf{S = \dfrac{n(n + 1)(2n + 1)}{6} }$

★ Formula to find the nth term of an AP is the square of the number of terms:

• $: \implies \sf{S = {n}^{2} }$

★ Formula to find the sum of of an AP:

• $: \implies \sf{S = n(n+1)}$

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Hope It Helps You!! :)