Question

find the sum of first 21 terms if middle term of an AP is 20

Answer 1

S21=?
a11=20
a11=a+10d
so, 20=a+10d

s21=21/2(2a+20d)
=21a+210d
=21(a+10d). (a+10d=20)
=21* 20
=420

Answer 2

Middle term = 11 = 20

So, a11 = a + 10d

      20 = a+10d               --------------------------- (1)


We know sum of n terms = n/2(a+(n-1)d)

Sum of first 21 terms =  21/2(2a+20d)

                                   = 21a + 210d

                                   = 21(a+10d)        --------- from (1)

                                    = 21 * 20

                                   = 420.


Hope this helps!