Question

find the missing term in AP
_,38,_,_,_,-22​

Answer 1

Answer:

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

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. Let's 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

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

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

Hope this helps ✌️

Answer 2

given = a2= 38 & a6 = -22

a2 = a + d

38 = a + d........(1)

a6 = -22

a + 5d = -22......(2)

a+d = 38

a + 5d = -22

USING ELIMINATION method

a + d = 38

a + 5d = -22

(-) (-) (+)

-4d = 16

d = -4

PUT THE VALUE OF D = -4

a + d = 38

a + (-4) = 38

a -4 = 38

a = 38 +4

a = 42

a = 42 & d = -4

a = 42

a2 = 38

a3 = a +2d

a3 = 42 +2(-4)

a3 = 42 -8

a3 = 34

a4 = a +3d

a4 = 42 + 3(-4)

a4 = 42 -12

a4 = 30

a5 = a + 4d

a5 = 42 + 4(-4)

a5 = 42 -16

a5 = 26

a6 = -22

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