Question

check whether 2019 a term of the A. S 5, 8, 11,....​

Answer 1

$Given \: sequence \: 5,8,11 \ldots$

$i) a_{2} - a_{1} = 8 - 5 = 3$

$ii) a_{3} - a_{2} = 11 - 8 = 3$

$\blue {a_{2} - a_{1} = a_{3} - a_{2} = 3}$

$\therefore Given \: sequence \: is \:an \:A.P$

$Now ,First \:term ( a ) = 5$

$Common \: difference (d) = 3$

$Let \: n^{th} \:term \: of \: A.P = 2019$

$\implies a + (n-1)d = 2019$

$\implies 5 + (n-1)\times 3 = 2019$

$\implies (n-1)\times 3 = 2019 - 5$

$\implies (n-1)\times 3 = 2014$

$\implies n-1= \frac{ 2014}{3}$

$\implies n= \frac{ 2014}{3} + 1$

$\implies n= \frac{ 2014 + 3}{3}$

$\implies n= \frac{ 2017}{3}$

$But \: \red{( Number \:terms \:of \: an \:A.P }$

$\red{ should \:not \:be \: a \: fraction) }$

Therefore.,

$\green { 2019 \: is \:not \: a \: term \:of }$

$\green { given \:A.P .}$

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