Question

2,5,8,......is an arithmetic sequence. how to find out the position of 134

Answer 1

Answer:

$\sf{134 \ is \ 45^{th} \ term.}$

Given:

$\sf{2, \ 5, \ 8 \ is \ an \ arithmetic \ sequence. }$

To find:

$\sf{The \ position \ 134.}$

Solution:

$\sf{2, \ 5, \ 8 \ is \ an \ arithmetic \ sequence. }$

$\sf{Here, \ a=2, \ d=5-2=3}$

$\boxed{\sf{t_{n}=a+(n-1)d}}$

$\sf{\therefore{134=2+(n-1)\times3}}$

$\sf{\therefore{3(n-1)=134-2}}$

$\sf{\therefore{3(n-1)=132}}$

$\sf{\therefore{n-1=\dfrac{132}{3}}}$

$\sf{\therefore{n-1=44}}$

$\sf{\therefore{n=44+1}}$

$\sf{\therefore{n=45}}$

$\sf\purple{\tt{\therefore{134 \ is \ 45^{th} \ term.}}}$

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$\sf\blue{Extra \ information:}$

$\sf{1. \ S_{n}=\dfrac{n}{2}[2a+(n-1)d]}$

$\sf{2. \ S_{n}=\dfrac{n}{2}[t_{1}+t_{n}]}$

$\sf{3. \ 2\times \ t_{2}=t_{1}+t_{3}}$

Answer 2

$\large{\boxed{\bf{AnswEr}}}$

• Position of 134 is 45th.

Given :-

• An arithmetic sequence as 2,5,8.

To Find :-

• Position of 134.

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$\large{\boxed{\bf{Solution}}}$

★ Here,

• a ➪ 2

• d ➪ 5 - 2 ➪ 3

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➪ $tn = a + (n - 1)d$

$= > 2 + (n - 1)3 = 134$

$= > 2 + 3n - 3 = 134$

$= > 3n - 1 = 134$

$= > 3n = 134 + 1$

$= > 3n = 135$

$= > n = \frac{135}{3}$

$= > n = 45$

Hence, the position of 134 is 45th.

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