If the 21st term of an AP is 25 find the sum of its 41 term. Created by kritikaThakur. Math

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

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July 2022 2 25 Report

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

JyotiMaxwell 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!