In an A.P. if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.
a = 22, d = -4
Sn = 64
64 = 
(2a + (n – 1) d)
n [44 – (n – 1)4] = 128
n (44 – 4n + 4) = 128
48n – 4n2 = 128
n2 – 12n + 32 = 0
n2 – 8n – 4n + 32 = 0
(n – 8) (n – 4) = 0
n = 8 or n = 4
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