(a) The fourth term of an A.P is 37 and 6th term is 12 more
MATHEMATICS
WAEC 1994
(a) The fourth term of an A.P is 37 and 6th term is 12 more than the fourth term . Find the first and seventh terms.
(b) If \(P = {1, 2, 3, 4}\) and \(Q = {3, 5, 6}\), find (i) \(P \cap Q\) ; (ii) \(P \cup Q\) ; (iii) \((P \cap Q) \cup Q\) ; (iv) \((P \cap Q) \cup P\).
Explanation
(a) \(T_{n} = a + (n - 1)d\) (nth term of an A.P)
\(T_{4} = a + 3d = 37 ... (1)\)
\(T_{6} = a + 5d = 12 + 37 = 49 ... (2)\)
(2) - (1) : \(2d = 12 \implies d = 6\)
\(a + 3d = 37 \implies a + 3(6) = 37\)
\(a + 18 = 37 \implies a = 37 - 18 = 19\)
\(T_{7} = a + 6d = 19 + 6(6) = 19 + 36 = 55\)
(b) \(P = {1, 2, 3, 4} ; Q = {3, 5, 6}\)
(i) \(P \cap Q = {3}\)
(ii) \(P \cup Q = {1, 2, 3, 4, 5, 6}\)
(iii) \((P \cap Q) \cup Q = {3, 5, 6}\)
(iv) \((P \cap Q) \cup P = {1, 2, 3, 4}\)
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