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  • Which term of the Arithmetic Progression –7, –12, –17, –22, ... will be –82? Is –100 any term of the A.P. ? Give reason for your answer.     <div

Which term of the Arithmetic Progression –7, –12, –17, –22, ... will be –82? Is –100 any term of the A.P. ? Give reason for your answer.

 

 
 
 
 
 

Answers (1)

AP = -7,-12, -17,-22,..., -82,...

Let a_n =- 82            a_1 =- 7\qquad d = -12 - (-7) = -5

a_n = a_1 +(n-1)d

-82 = -7 +(n-1)(-5)

\frac{75}{5} = n-1\Rightarrow n = 16

Again, -100 = a_m = -7 + (m-1)(-5)

\Rightarrow (m-1)(-5) = -93 \Rightarrow m = \frac{93}{5} + 1\notin N

So, -100 is not a term of given A.P

 

Posted by

Safeer PP

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