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


(ii)to 12 terms


Sn = [2a + (n – 1) d]


= [2 + (12 – 1) 2]


= 6 (2 + 22)


= 144


(iii)to 25 terms


Sn = [2a + (n – 1) d]


= [2 (3) + 24()]


= [6 + 36]


= 525


(iv)to 12 terms


Sn = [2a + (n – 1) d]


= [82 - 55]


= 6 [27] = 162


(v)to 22 terms


Sn = [2a + (n – 1) d]


= [2(a + b) + (21) (-2b)]


= 11 [2a + 2b – 42b]


= 11 [2a – 40b]


= 22a – 440b


(vi)to n terms


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]


(vii)to n terms


Sn = [2a + (n – 1) d]


= [2() + (n – 1) xy]


= {2(x – y) + (n – 1) (2x – y)}


= {n (2x – y) – y}


(viii)to 36 terms


Sn = [2a + (n – 1) d]


= [-52 + (35) 2]


= 18 [-52 + 70]


= 18 [18] = 324


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