Question

Which term of the AP 21 18 15....is -81

Answer 1

AnswEr:-

35th term of the AP is -81

Step by Step Explanation :-

Given :-

First Term (a) = 21

Common Difference(d) = $\sf \; a_2 \;-\;a_1$

$:\implies\sf \; 18 \;-\;21$

$:\implies\sf\; 3$

$:\implies\sf\;d = -3$

$\rule{150}2$

To find :-

nth term

Finding :-

By using the Formula :-

$\large\boxed{\sf{\red{an = a\;+\; ( n \;-\;1)d}}}$

Here,

$:\implies\sf \;an = -81$

$:\implies\sf \;a = 21$

$:\implies\sf \;d = - 3$

$\rule{150}2$

Putting Values :-

$:\implies\sf \; -81 = 21 +\;(n\; - \:1)\;-3$

$:\implies\sf \; -81 = 21 + \; 3n \; - \; 3$

$:\implies\sf \; -81 = 24 \;-\; 3n$

$:\implies\sf \; -105 = \;-3n$

$:\implies\sf \; n = \dfrac{- 105}{-3}$

$:\implies\large\boxed{\sf {\pink{n = 35}}}$

Hence, The 35th term of the Given AP is -81.

$\rule{150}2$

Answer 2

$\huge \sf \fcolorbox{red}{pink}{Solution :)}$

Given ,

• First term = 21
• Common difference = - 3
• nth term = -81

We know that , the first nth term of an AP is given by

$\large \sf \fbox{a_{n} = a + (n - 1)d}$

Substitute the known values , we get

$\sf \hookrightarrow - 81 = 21 + (n - 1)( - 3) \\ \\ \sf \hookrightarrow - </em><em>102</em><em> = (n - 1)( - 3) \\ \\ \sf \hookrightarrow </em><em>34 </em><em>= (n - 1) \\ \\ \sf \hookrightarrow n = </em><em>34 </em><em>+ 1 \\ \\ \sf \hookrightarrow n = </em><em>35</em><em>$

Hence , 35 term of an AP is - 81

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