Question

Find the sum of the first 21 terms of an A.P whose middle term is 20.

Answer 1

here,
n=21
(a1 + a21)/2 = 20
=(a1 + a11)= 40
 
sum of ap =n(a1+a11)/2
                 =21*40/2
                 =840/2
                  = 420 

Answer 2

Let first term be a

common difference be d

S21 =?

middle term T11 = 20

So T11 = a +(11-1)d

20 = a +10d

a = 20-10d__________(1)

S21 = 21/2 [2a +(21-1)d

= 21/2[2a +20d]________(2)

Put the value of equation (1) in (2)

= 21/2 [2(20-10d)+20d]

= 21/2[40-20d+20d]

= 21/2[40]

= 420 __________Answer