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Q.

The sum of the fourth and fifth term of an AP is 24 and the sum of the sixth and the tenth term of an AP is 44. Find the first three term of an AP.

Class: 10

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a

102

b

\frac{102}{7}

c

10

d

None

answer is B.

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Detailed Solution

Here,
a4 = a + 3d   …(1)
a5 = a + 4d   …(2)
Therefore,
a4 + a5 = 24
a + 3d + a + 4d = 24   [from (1) & (2)]
2a + 7d = 24   …(3)
Again, a6 = a + 5d   …(4)
a10 = a +9d   …(5)
Therefore, a6 + a10 = 44
a + 5d + a + 9d = 44   [from (4) & (5)]
2a + 14d = 44
a + 7d = 22   …(6)
Substituting eq (3) & (6), we get d = 20/7, a = 2
Therefore,
a1 = 2
a2 = a + d = 2+20/7 = 34/7
a3 = a + 2d =

2 + 2 \times 20 / 7 = 54 / 7

First three term of an AP =

2 + \frac{34}{7} + \frac{54}{7} = \frac{102}{7}

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