Question

Which term of the series :

21, 18, 15, ............. is -81 ?

Can any term of this series be zero ?

If yes, find the number of terms.

Answer 1

A = 21

d = 18 - 21 = -3 .

Let 0 be the n th term.


Now,


0 = 21 + ( n -1 ) -3

0 = 21 -3n + 3

0 = 24-3n

3n = 24

n = $\frac{24}{3}$ = 8 .

Therefore, the 8th term is zero.


also
applying
Tn=a+(n-1)d
-81=21+(n-1)(-3)

-102=-3$\times$(n-1)
34=n-1
n=35