# The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

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The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

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Solution:

Let the first term of an A.P = a
and the common difference of the given  A.P = d
As we know that
an = a+(n-1) d
a4 = a +( 4-1) d
a4 = a+3d
Similarly ,
a8 = a + 7 d
a6  = a + 5 d
a10 = a+ 9d
Sum of 4th and 8th terms of an A.P = 24 ( given )
a4 +a8 = 24
a + 3d + a + 7d = 24
2a + 10 d = 24
a +5d = 12  .....................(i)
Sum of 6 th and 10 th term  of an A.P = 44 ( given )
a6 +a10 = 44
a + 5d +a+ 9d = 44
2a + 14 =44
a + 7d = 22  .....................(ii)
Solving (i) & (ii)
a +7 d  = 22
a + 5d = 12
-   -       -

2d  = 10
d = 5
From equation (i) ,
a + 5d = 12
a + 5 (5) = 12
a+25= 12
a = - 13
a2 = a+d = -13+5 = -8
a3 = a2 + d = -8+5 = -3
So, the first three terms are -13 ,-8,-3

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