Question

Which term of the A.P: 21, 18, 15,...... is -81. Also, is any term 0?

Answer 1

Answer:

answers for the given problems are given

Answer 2

Question :–

Which term of the A.P: 21, 18, 15,...... is -81. Also, is any term 0?

Solution :–

First term (a) = 21

Common difference (d) = $\sf a_{2} - a_{1}$

= 18 - 21

= -3

• d = -3

$\sf {n}^{th}$ term is -81

$\sf {n}^{th}$ = a + (n - 1)d

-81 = 21 + (n - 1)(-3)

-81 = 21 - 3n + 3

-81 = 24 - 3n

3n = 24 + 81

3n = 105

n = $\sf \frac{\cancel{105}}{\cancel{3}}$

n = 35

Hence,

$\boxed {\sf \pink{{35}^{th} \: term \: is \: 35}}$

$\sf {0}^{th}$ term = a + (n - 1)d

0 = 21 + (n - 1)(-3)

0 = 21 - 3n + 3

0 = 24 - 3n

3n = 24

n = $\sf \frac{\cancel{24}}{\cancel{3}}$

n = 8

Hence,

$\boxed{\sf \pink{ {8}^{th} \: term \: is \: 0}}$