Which term of the AP: 21, 18, 15, ... is - 81? Also, is 0 a term of this AP? Give reasons for your answer. Class 9

Which term of the AP: 21, 18, 15, ... is - 81? Also, is 0 a term of this AP? Give reasons for your answer. Class 9

Question 1.

Which term of the AP: 21, 18, 15, ... is - 81? Also, is 0 a term of this AP? Give reasons for your answer. Class 9

Solution:

The given AP is 21, 18, 15,...

a = 21, d = 18 - 21 = -3

t_n = a + (n -1) d

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

t_n = 21 - 3 (n -1)

i. Let t_n = -81

∴ -81 = 21 - 3(n - 1)

∴ -81 - 21 = -3(n -1)

∴ -102 = -3(n -1)

∴ n - 1 = $\frac{-102}{-3}$

∴ n -1 = 34

∴ n = 35

∴ 35^th term of the AP is -81.

ii. Let t_n = 0

∴ 0 = 21 - 3(n -1)

∴ -21 = -3 (n -1)

∴ $\frac{21}{3}$ = n - 1

∴ n - 1 = 7

∴ n = 8

Since n = 8 is a natural number,

∴ 0 is a term of the AP.