Question

pls solve in easiest way and explain?solve in notebook and give the photo pls.
pls answer as per class 10 th.​

Answer 1

Step-by-step explanation:

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Answer 2

$\sf\blue{Question:}$

$\sf{Find \ the \ 20^{th} \ term \ of \ A.P. \ whose}$

$\sf{third \ term \ is \ 7 \ and \ the \ seventh}$

$\sf{term \ exceeds \ three \ times \ the \ 3^{rd}}$

$\sf{term \ by \ 2. \ Also \ find \ it's \ n^{th} \ term(an).}$

__________________________________

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{20^{th} \ term \ is \ 75 \ and}$

$\sf{n^{th} \ term \ is \ -1+4(n-1).}$

$\sf\orange{Given:}$

$\sf{In \ an \ A.P.,}$

$\sf{\implies{a3=7}}$

$\sf{\implies{a7=3\times \ a3+2}}$

$\sf\pink{To \ find:}$

$\sf{1. \ a20}$

$\sf{2. \ an}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{a3=7...(1)}$

$\sf{\therefore{a7=3(7)+2}}$

$\sf{\therefore{a7=23...(2)}}$

$\sf{an=a+(n-1)d... formula}}$

$\sf{...from \ (1) \ and \ (2)}$

$\sf{a+2d=7...(1)}$

$\sf{a+6d=23...(2)}$

$\sf{Subract \ equation(1) \ from \ equation (2)}$

$\sf{a+6d=23}$

$\sf{-}$

$\sf{a+2d=7}$

____________________

$\sf{4d=16}$

$\boxed{\sf{\therefore{d=4}}}$

$\sf{Substitute \ in \ equation (1)}$

$\sf{a+2\times(4)=7}$

$\sf{\therefore{a+8=7}}$

$\sf{a=7-8}$

$\boxed{\sf{\therefore{a=-1}}}$

$\sf{By \ formula}$

$\boxex{sf{an=a+(n-1)d}}$

$\sf{a20=-1+(20-1)\times(4)}$

$\sf{a20=-1+19\times4}$

$\sf{a20=-1+76}$

$\sf{a20=75}$

$\sf{an=-1+(n-1)\times4}$

$\sf{an=-1+4(n-1)}$

$\sf\purple{\tt{\therefore{20^{th} \ term \ is \ 75 \ and}}}$

$\sf\purple{\tt{n^{th} \ term \ is \ -1+4(n-1).}}$