Find the sum of the following arithmetic progressions:
(i)
to 10 terms
(ii)
to 12 terms
(iii)
to 25 terms
(iv)
to 12 terms
(v)
to 22 terms
(vi)
to n terms
(vii)
to n terms
(viii)
to 36 terms
(i)
to 10 terms
Sn = 
[2a + (n – 1) d]
S10 = 
[100 + 9(-4)]
= 5 [100 – 36]
= 5(64) = 320
Sn = 
[2a + (n – 1) d]
= 
[2 + (12 – 1) 2]
= 6 (2 + 22)
= 144
Sn = 
[2a + (n – 1) d]
= 
[2 (3) + 24(
)]
= 
[6 + 36]
= 525
Sn = 
[2a + (n – 1) d]
= 
[82 - 55]
= 6 [27] = 162
Sn = 
[2a + (n – 1) d]
= 
[2(a + b) + (21) (-2b)]
= 11 [2a + 2b – 42b]
= 11 [2a – 40b]
= 22a – 440b
Sn = 
[2a + (n – 1) d]
= 
[2(x – y)2 + (n – 1) (2xy)]
= 
(2) [(x – y)2 + (n – 1) xy]
= n [(x – y)2 + (n – 1) xy]
Sn = 
[2a + (n – 1) d]
= 
[2(
) + (n – 1) xy]
= 
{2(x – y) + (n – 1) (2x – y)}
= 
{n (2x – y) – y}
Sn = 
[2a + (n – 1) d]
= 
[-52 + (35) 2]
= 18 [-52 + 70]
= 18 [18] = 324