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in Arithmetic Progression by (49.2k points)
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The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.

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Given, a4 + a8 = 24 (i)

a6 + a10 = 44 (ii)

We know, an = a + (n – 1) d

4 th term, a4 = a + 3d

6 th term, a6 = a + 5d

8 th term, a8 = a + 7d

10th term, a10 = a + 9d

Putting the value of a4 and a8 in (i), we get

a + 3d + a + 7d = 24

2a + 10d = 24 (iii)

Put the value of a6 and a10 in (ii), we get

a + 5d + a + 9d = 44

2a + 14d = 44 (iv)

By subtracting (iii) from (iv), we get

4d = 20

d = 5

Now putting value of d in (iii), we get

2a = 24 – 10(5)

a = -13

a1 = -13

a2 = a + d = -13 + 5 = - 8

a3 = a + 2d = -13 + 10 = -3

Hence, the A.P. is -13, - 8, - 3,…

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