Question

Is zero is the term of the AP-81,-76,-71.......​

Answer 1

Answer:

no 0 is not term of given AP

Answer 2

$Given \: A.P : -81 , -76, -71 , \ldots$

$First\:term (a_{1}) = a = -81$

$Common \: difference (d) = a_{2} - a_{1} \\= -76 - ( - 81 ) \\= -76 + 81 \\= 5$

$\boxed { \pink{ n^{th} \: term (a_{n}) = a + (n-1)d }}$

$Let \: n^{th} \: term = 0$

$\implies -81 + ( n - 1 ) 5 = 0$

$\implies ( n - 1 ) 5 = 81$

$\implies ( n - 1 ) = \frac{81}{5}$

$\implies n = \frac{81}{5} + 1$

$\implies n = \frac{81+ 5}{5}$

$\implies n = \frac{86}{5} \: \pink { (not \: a \: natural\: number ) }$

Therefore.,

$\green { Zero \: is \: not \: a \:term \: in } \green { given \:A.P }$

♪•••