Theory question 111
Progressions(a) The fourth term of an A.P. is 37 and the 6th term is 12 more than the fouth term. Find the first and seventh terms
(b) If P = (1,2,3,4) and Q = (3,5,6), find: (i) P∩Q; (ii) P∪Q (iii) (P∩Q)∪Q; (iv) (P∪Q)∩P.
Show the model answer
Model answer
(a) a + 3d = 37 and (a + 5d) − (a + 3d) = 12, so 2d = 12, d = 6
a = 37 − 18 = 19 (first term); seventh term = 19 + 6 × 6 = 55
(b)(i) P∩Q = {3}
(ii) P∪Q = {1, 2, 3, 4, 5, 6}
(iii) (P∩Q)∪Q = {3, 5, 6}
(iv) (P∪Q)∩P = {1, 2, 3, 4}
Explanation
nth term of an A.P. is a + (n − 1)d.