#### Question

In the following APs, find the missing terms in the boxes :

#### Solution

For this A.P.,

a_{2} = 38

a_{6} = −22

We know that

a_{n} = a + (n − 1) d

a_{2} = a + (2 − 1) d

38 = a + d (1)

a_{6} = a + (6 − 1) d

−22 = a + 5d (2)

On subtracting equation (1) from (2), we obtain

− 22 − 38 = 4d

−60 = 4d

d = −15

a = a_{2} − d = 38 − (−15) = 53

a_{3} = a + 2d = 53 + 2 (−15) = 23

a_{4} = a + 3d = 53 + 3 (−15) = 8

a_{5} = a + 4d = 53 + 4 (−15) = −7

Therefore, the missing terms are 53, 23, 8, and −7 respectively.

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Solution In the following APs, find the missing terms in the boxes Concept: nth Term of an AP.