2023
Mathematics
JAMB
The third term of an A.P is 6 and the fifth term is 12. Find the sum of its first twelve terms
A.
201
B.
144
C.
198
D.
72
Correct Answer: 198
Explanation
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
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 = 198THIS WEEK's
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