Q. 18 I3.7( 9 Votes )

# In the following A.P., find the missing terms:□, 38, □,□,□, – 22

Given: a2 = 38 and a6 = –22

We know that,

an = a + (n – 1)d

a2 = a + (2 – 1)d

38 = a + d …(i)

and a6 = a +(6 – 1)d

–22 = a + 5d …(ii)

Solving linear equations (i) and (ii), we get

a + d – a – 5d = 38 – (–22)

–4d = 60

d = –15

Putting the value of d in eq. (i), we get

a + (–15) = 38

a – 15 = 38

a = 53

Now, a3 = a + 2d = 53 + 2(–15) = 53 – 30 = 23

a4 = a + 3d = 53 + 3(–15) = 53 – 45 = 8

a5 = a + 4d = 53 + 4(–15) = 53 – 60 = –7

Hence, the missing terms are 53, 23, 8 and –7

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