If the sum of first 4 terms of an arithmetic progression is p,the sum of the first 8 terms is q and the sum of the first 12 terms is r,express 3p r in terms of q.
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Tn = a + (n-1) d
Sn = [ 2 a + (n-1) d ] n/2
p = [ 2 a + 3 d ] 2 = 4a + 6 d -- equation 1
q = [ 2 a + 7 d ] 4 = 8a + 28 d --- equation 2
r = [ 2a + 11 d ] 6 = 12 a + 66 d -- equation 3
3 p + r = 24 a + 84 d = 3 q
Sn = [ 2 a + (n-1) d ] n/2
p = [ 2 a + 3 d ] 2 = 4a + 6 d -- equation 1
q = [ 2 a + 7 d ] 4 = 8a + 28 d --- equation 2
r = [ 2a + 11 d ] 6 = 12 a + 66 d -- equation 3
3 p + r = 24 a + 84 d = 3 q
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