Question

In the following AP find the missing term _,-38,_,_,_,-22 ​

Answer 1

Answer:

Step-by-step explanation:

In this problem, we are given 2nd and 6th term.

 

Using formula an=a+(n−1)d,   to find nth term of arithmetic progression, we get

 

a2=a+(2−1)d     And      a6=a+(6−1)d

 

⇒38=a+d   And    −22=a+5d

 

These are equations in two variables, we can solve them using any method. Lets solve them using substitution method.

 

Using equation (38=a+d), we can say that a=38−d. Putting value of a in equation (−22=a+5d),  we get

 

−22=38−d+5d

 

⇒4d=−60

 

⇒d=−604=−15

 

Using this value of d and putting this in equation 38=a+d, we get

38=a−15

 

⇒a=53

 

Therefore, we get a=53 and d=−15

 

First term = a = 53

 

Third term = second term + d = 38 - 15 = 23

 

Fourth term = third term + d = 23 - 15 = 8

 

Fiftht term = fourth term + d =  8 - 15 = -7

 

Therefore, missing terms are 53, 23, 8 and -7.