Question

Example 5. The sum of n terms of an A.P. is n^2+ 2n. Find the series.​

Answer 1

Answer:

The sum of n terms of an A.P. is n^2 + 2n

Step-by-step explanation:

If we take n = 2 , the sum will be (Sn = 2^2 + 2×2)

= 8

Sn = 8, n=2

Putting it into the equation

Sn = n/2(2a + (n-1)d)

8 = 2/2 (2a + (2-1)d)

8 = 2a + d - eqn no. 1

Now if we take n = 3, we get 3^2 + 2×3 = 15

Sn = 15 , n= 3

Putting it into sum equation

Sn = n/2(2a + (n-1)d)

15 = 3/2 (2a +(3-1)d)

15 = 3/2 (2a +2d)

30 = 3(2a +2d)

30 = 6a + 6d - eqn no. 2

eqn no.1 (8 = 2a + d)

eqn no.2 (30 = 6a + 6d)

change eqn. no1 to make a or d equivalent to eqn no.2

(8 = 2a + d) multiplied by 3,

we get 24 = 6a + 3d. eqn no. 3

Now subtract eqn no. 3 from eqn no. 2

30 = 6a + 6d

-24 = -6a - 3d

= 6 = 3d

now d = 6/3 = 2

putting d = 2 in eqn no. 1

8 = 2a + 2

6 = 2a

a = 3

So the series is :

3 , 5 , 7, 9, 11, 13..........