Question

if 4 th and 6 th terms of an AP be 15 and 23 respectively then 83 is which term​

Answer 1

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$\underline{\blacksquare\:\:\:\footnotesize{\red{\text{SOLUTION:-}}}}$

$\footnotesize{a_4=a_1+(4-1)d}$

$\footnotesize{15=a_1+3d}$

$\footnotesize{a_1+3d=15}$

$\footnotesize{a_1=15-3d\:\:------------(1)}$

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$\footnotesize{a_6=a_1+(6-1)d}$

$\footnotesize{23=a_1+5d}$

$\footnotesize{a_1+5d=23}$

$\footnotesize{a_1=23-5d\:\:------------(2)}$

$\footnotesize{\text{compairing equation (1) and (2) we get ,}}$

$\footnotesize{15-3d=23-5d}$

$\footnotesize{5d-3d=23-15}$

$\footnotesize{2d=8}$

$\footnotesize{d=\dfrac{\cancel8}{\cancel2}}$

$\footnotesize{\red{d=4}}$

$\footnotesize{\text{putting value d=4 in equation (1) , we get}}$

$\footnotesize{a_1=15-3(4)}$

$\footnotesize{a_1=15-12}$

$\footnotesize{\red{a_1=3}}$

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$\footnotesize{\text{let , 83 be the n'th term of the series }}$

$\footnotesize{a_n=a_1+(n-1)d}$

$\footnotesize{83=3+(n-1)4}$

$\footnotesize{83-3=(n-1)4}$

$\footnotesize{\dfrac{\cancel{80}}{\cancel4}=(n-1)}$

$\footnotesize{20=(n-1)}$

$\footnotesize{20+1=n}$

$\footnotesize{\red{n=21}}$

$\footnotesize{\therefore\:\text{83 is the 21'th term of the series }}$

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