# the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

Let the first term of an A.P.=a

and the common difference of the given A.P.=d

As we know that,

a n = a + (n − 1) d

a 4 = a + (4 − 1) d

a 4 = a + 3d

Similarly,

a 8 = a + 7d

a 6 = a + 5d

a 10 = a + 9d

Sum of 4th and 8th term =  24  (Given)

a 4 + a 8 = 24

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12.................... (i)

Sum of 6th and 10th term = 44  (Given)

a 6 + a 10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 ......................(ii)

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

From equation (i), we get,

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13

a 2 = a + d = − 13 + 5 = −8

a 3 = a 2 + d = − 8 + 5 = −3

The first three terms of this A.P. are −13, −8, and −3.

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a+3d+a+7d=24

= 2a+10d=24

now dividing the equation by 2 we get,

a+5d=12  ....................... equation 1

Also given,

a+5d+a+9d=44

= 2a+14d=44

now diving the equation throughout by 2 we get,

a+7d=22  .........................  equation 2

Now equation equation 1 and 2

we get

d=5 and a=-13

therfore the a.p=-13,-8,-3

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Therefore,

a+3d + a+7d=24             and             a+5d + a+9d=44

2a+10d=24----------> (i)                       2a+14d=44--------->(ii)

Subtracting (i) from (ii),

2a+14d-2a-10d=44-24

4d=20

d=5

so, using d in (i)

2a + 50 = 24

2a= -26

a= -13

First 3 terms = -13, -8, -3

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