Question

Which term of the A.P. $84,80,76,.........$ is $0$?

Answer 1

Given A.P is

$84,80,76,.....$

first term of this A.P is $a_1=84$

second term of this A.P is $a_2=80$

common difference of an A.P is given by

$(i.e.,d=a_{n+1}-a_n)$

putting n=1 in above equation

$d=a_2-a_1=80-84=-4$

hence common difference for this A.P is $d=-4$

the nth term of an A.P is given by.

$a_n=a_1+(n-1)d$

$⟹a_n=84+(n-1)(-4)$

$⟹a_n=84-4n+4$

$⟹a_n=88-4n...eq\left(1\right)$

we have to find which term$\left(n\right)$ of this A.P is $a_n=0$

put $a_n=0$ in eq(1)

$⟹0=88-4\times n$

$⟹4\times n=88$

$⟹n=\frac{88}{4}$

$⟹n=22$

hence $22$th term of this A.P is $0$