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,…