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

1.	Check whether 2019 a term of the A. S 5, 8, 11,....
Answer» $Given \: sequence \: 5,8,11 \ldots$ $i) a_{2} - a_{1} = 8 - 5 = 3$ $ii) a_{3} - a_{2} = 11 - 8 = 3$ $\blue {a_{2} - a_{1} = a_{3} - a_{2} = 3}$ $\<klux>THEREFORE</klux> Given \: sequence \: is \:an \:A.P$ $Now ,First \:term ( a ) = 5$ $Common \: difference (d) = 3$ $Let \: n^{th} \:term \: of \: A.P = 2019$ $\implies a + (n-1)d = 2019$ $\implies 5 + (n-1)\times 3 = 2019$ $\implies (n-1)\times 3 = 2019 - 5$ $\implies (n-1)\times 3 = 2014$ $\implies n-1= \frac{ 2014}{3}$ $\implies n= \frac{ 2014}{3} + 1$ $\implies n= \frac{ 2014 + 3}{3}$ $\implies n= \frac{ 2017}{3}$ $But \: \red{( Number \:terms \:of \: an \:A.P }$ $\red{ should \:not \:be \: a \: fraction) }$ Therefore., $\green { 2019 \: is \:not \: a \: term \:of }$ $\green { given \:A.P .}$ •••♪

Answer»

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