Given: a2 = 8 and a4 = 14 and n = 21
We know that,
a2 = a + d = 8 …(i)
and a4 = a + 3d = 14 …(ii)
Solving the linear equations (i) and (ii), we get
a + d – a – 3d = 8 – 14
⇒ -2d = -6
⇒ d = 3
Putting the value of d in eq. (i), we get
a + 3 = 8
⇒ a = 8 – 3 = 5
Now, we have to find the sum of first 21 terms.
⇒ S21 = 21 [5 + 10 × (3)]
⇒ S21 = 21 [35]
⇒ S21 = 735