Question

If the 21st term of an AP is 25 find the sum of its 41 term

Answer 1

a+ 20d=25

Sum=41/2(2a+40d)

Sum= 41/2(2(a+20d)) = 41/2(2×25)

=. 1025

Answer 2

We know that nth term of an AP is given by an = a + (n - 1) * d.

21st term a21 = a + (21 - 1) * d

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


Given that 21st term of an AP is 25.

a + 20d = 25

a = 25 - 20d  -------- (2)


We know that sum of n terms of an AP sn = n/2(2a + (n - 1) * d).

41st term s41 = 41/2(2(25 - 20d) + (41 - 40) * d

                       = 41/2(2(25 - 20d) + 40d)

                       = 41/2(50 - 40d + 40d)

                       = 41/2(50)

                       = 41 * 25

                        = 1025.


Therefore the sum = 1025.


Hope this helps!