Given: a2 = 9 and a4 = 21 and n = 25
We know that,
a2 = a + d = 9 …(i)
and a4 = a + 3d = 21 …(ii)
Solving the linear equations (i) and (ii), we get
a + d – a – 3d = 9 – 21
⇒ -2d = -12
⇒ d = 6
Putting the value of d in eq. (i), we get
a + 6 = 9
⇒ a = 9 – 6 = 3
Now, we have to find the sum of first 25 terms.
⇒ S25 = 25 [3 + 12 × (6)]
⇒ S25 = 25 [75]
⇒ S25 = 1875
