Question

Ap.21,18,15..……which term of an ap -81

Answer 1

$d = - 3 \\ - 81 = 21 + (n - 1)( - 3 ) \\ - 102 = (n - 1)( - 3) \\ 34 = n - 1 \\ n = 35$

Answer 2

Given: An arithmetic progression.

To find: The term in the AP that equates to - 81.

Answer:

AP: 21, 18, 15, ...

From the given progression, we have:

• The first term (a) = 21.
• The common difference (d) = 18 - 21 = - 3.

Since we have to find the term in the AP that equates to - 81,

$\Longrightarrow\ \sf\ a_n\ =\ -\ 81\\\\\\\implies\ a\ +\ (n\ -\ 1)d\ =\ -\ 81\\\\\\\implies\ 21\ +\ (n\ -\ 1)(-3)\ =\ -\ 81\\\\\\\implies\ 21\ -\ 3n\ +\ 3\ =\ -\ 81\\\\\\\implies\ 24\ -\ 3n\ =\ -\ 81\\\\\\\implies\ -\ 3n\ =\ -\ 81\ -\ 24\\\\\\\implies\ -\ 3n\ =\ -\ 105\\\\\\\implies\ n\ =\ \dfrac{-105}{-3}\\\\\\\implies\ n\ =\ 35$

Therefore, the 35th term of the AP = - 81.