Q. 18 I3.7( 9 Votes )

In the following A.P., find the missing terms:

, 38, ,,, – 22

Answer :

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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