Sir\Madam please explain me this question on Arithmetic Progressions!

Let no. of terms = 2n
First term = a
Common diff = d

First odd term = a
Last odd term = a + (2n - 2)d
Common difference between odd terms = 2d
No of odd terms = 2n/2 = n
Sum of odd terms = n/2[a + a + (n-2)d]
Þ 24= n/2(2a + (n - 2)d)..............(1)

Last term = a + (2n -1)d
According to question, we have

 

Last term = a + 21/2
⇒ a + (2n-1)d -a =21/2

⇒    (2n-1)d = 21/2..........(2)

First even term = a + d
Last even term = a + (2n-1)d = a + 21/2
Common diff between even terms = 2d
No of even terms = n
Sum of even terms= n/2 (a+a+(2n-1)d)
30 = n/2(2a + 21/2).........(3)

 

On solving (1), (2) and (3), we get n = 8.

 

Hence the series is 3/2, 3, 9/2, 6, 15/2, 9, 21/2, 12