Math, asked by prashant7487, 1 year ago

find the value of x,when in the ap.given below_2+6+10...+x=1800

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Answered by MdSaalikFaizan

2+6+10+x=1800

18+x=1800

x=1800-18

x=1782

Hope the answer is helpful !!

Good Day !!

prashant7487: bhai wrong ha answer

MdSaalikFaizan: kaise?

prashant7487: bhai ye to mujhe bhi nhi pata

prashant7487: bhai yar kuch tips da da science ka liya

shadowsabers03: I'll say how you've mistaken.

shadowsabers03: In the question it is 2 + 6 + 10 + ... + x = 1800. Here are three dots after 10 +, which means the AP is continuing and there are many terms between 10 and x.

But you've answered it as 2 + 6 + 10 + x = 1800, in which you've considered that the next term after 10 is x, and there is no term between 10 and x. This is the mistake.

MdSaalikFaizan: ohh....got it

MdSaalikFaizan: bhai science k liye khud k notes bna aur usse padh

MdSaalikFaizan: mera v kl science ka xam h

Answered by shadowsabers03

$a=2 \\ \\ d=6-2=4 \\ \\ \\ a_n=dn+a-d \\ \\ \Rightarrow\ a_n=4n+2-4 \\ \\ \Rightarrow\ a_n=4n-2 \\ \\ \\ $\sf{Let}$\ \ x=a_n=4n-2$

$2+6+10+...+x=1800 \\ \\ \Rightarrow\ 2+6+10+...+4n-2=1800 \\ \\ \Rightarrow\ \frac{n}{2}[2+4n-2]=1800\ \ \ \ \ \ \ \ \ \ [S_n=\frac{n}{2}[a+a_n]] \\ \\ \Rightarrow\ 2n^2 =1800 \\ \\ \Rightarrow\ n^2=900 \\ \\ \Rightarrow\ n=30\ \ \ \ \ \ \ \ \ \ \ \underline{\overline{\text{OR}}} \ \ \ \ \ \ \ \ \ \ \ n=-30\ ($\sf{not possible}$)$

$x=4n-2=4 \times 30 - 2 = 120-2=\bold{118}$

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