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

# 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

1. A
102
2. B
$\frac{102}{7}$
3. C
10
4. D
None

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### 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 =
First three term of an AP =$2+\frac{34}{7}+\frac{54}{7}=\frac{102}{7}$

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