The third term of an A.P is 6 and the fifth term is 12. F...
The third term of an A.P is 6 and the fifth term is 12. Find the sum of its first twelve terms
201
144
198
72
Correct answer is C
T3 = 6
T5 = 12
S12 = ?
Tn = a + (n - 1)d
⇒ T3 = a + 2d = 6 ----- (i)
⇒ T5 = a + 4d = 12 ----- (ii)
Subtract equation (ii) from (i)
⇒ -2d = -6
⇒ d−6−2 = 3
Substitute 3 for d in equation (i)
⇒ a + 2(3) = 6
⇒ a + 6 = 6
⇒ a = 6 - 6 = 0
Sn = n(2a+(n−1)d)2
⇒ S12 = 12(2×0+(12−1)3)2
⇒ S12 = 6(0 + 11 x 3)
⇒ S12 = 6(33)
∴ S12 = 198
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