Q. 18 G5.0( 2 Votes )

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

, , 13, , , 22

Answer :

Given: a3 = 13 and a6 = 22


We know that,


an = a + (n – 1)d


a3 = a + (3 – 1)d


13 = a + 2d …(i)


and a6 = a +(6 – 1)d


22 = a + 5d …(ii)


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


a + 2d – a – 5d = 13 – 22


–3d = 9


d = 3


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


a + 2(3) = 13


a + 6 = 13


a = 7


Now, a2 = a + d = 7 + 3 = 10


a4 = a + 3d = 7 + 3(3) = 7 + 9 = 16


a5 = a + 4d = 7 + 4(3) = 7 + 12 = 19


Hence, the missing terms are 7, 10, 16 and 19


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