Plot (-4, -3) (5, -7) and draw a line between them. Also plot (-4, -8) (5, -7) and
Draw a line between them. What is the coordinates of the point of intersection?
Answers
Answer:
AnswEr :
\begin{gathered}\bf{Given}\begin{cases}\sf{First \ term \ (a) = 17}\\\sf{Common \ difference \ (d) = 9}\\ \sf{Last \ term \ (a_{n})= 350}\end{cases}\end{gathered}
Given
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First term (a)=17
Common difference (d)=9
Last term (a
n
)=350
{\dag}\underline{\frak{Using \ Arithmetic \ progression \ formula \ :}}†
Using Arithmetic progression formula :
\star\:\small\boxed{\sf{\purple{a_{n} = a + [n - 1] d}}}⋆
a
n
=a+[n−1]d
\begin{gathered}:\implies\sf 17 + (n - 1)9 = 350 \\\\\\:\implies\sf (n - 1)9 = 350 - 17 \\\\\\:\implies\sf (n - 1)9 = 333 \\\\\\:\implies\sf n - 1 = \dfrac{\cancel{333}}{\cancel{9}} \\\\\\:\implies\sf n - 1 = 37 \\\\\\:\implies\sf n = 37 + 1 \\\\\\:\implies\boxed{\sf{\purple{ n = 38}}}}\end{gathered}
\therefore\underline{\sf{Here, \ we \ get \ n \ is \ 38.}}∴
Here, we get n is 38.
There are 38 terms in AP.
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{\dag}\underline{\frak{To \ find \ sum \ of \ an \ Arithmetic \ progression \ formula \ is \ given \ as \ : }}†
To find sum of an Arithmetic progression formula is given as :
\star\:\boxed{\sf{\purple{\Bigg(S_{n} = \dfrac{n}{2} (a + l) \Bigg)}}}⋆
(S
n
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2
n
(a+l))
\begin{gathered}:\implies\sf S_{38} = \dfrac{\cancel{38}}{\cancel{2}} = (17 + 350) \qquad \quad \bigg\lgroup\bf n = 38 \bigg\rgroup\\\\\\:\implies\sf 19 \times 367 \\\\\\:\implies\boxed{\sf{\purple{S_{n} = 6973}}}\end{gathered}
:⟹S
38
=
2
38
=(17+350)
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n=38
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:⟹19×367
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S
n
=6973
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⠀⠀⠀\boxed{\bf{\mid{\overline{\underline{\bigstar\: Used \ Formulas \ : }}}}\mid}
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★Used Formulas :
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\begin{gathered}\begin{lgathered}\boxed{\begin{minipage}{15 em}$\sf \displaystyle \bullet a_n=a + (n-1)d \\\\\\ \bullet S_n= \dfrac{n}{2} (a + a_n)$\end{minipage}}\end{lgathered}\end{gathered}