Theory question 102
Progressions(a) The 6th term of an A.P. is 35 and the 13th term is 77. Find the 20th term.
(b) The Venn diagram represents three subsets P, Q and R of the universal set U. Copy the Venn diagram. Shade and indicate the regions represented by: (i) P∩Q'∩R (ii) P'∩Q∩R'.
Show the model answer
Model answer
(a) a + 5d = 35 and a + 12d = 77. Subtract: 7d = 42, d = 6; a = 35 − 30 = 5.
T20 = a + 19d = 5 + 114 = 119.
(b)(i) P∩Q'∩R: the part common to P and R that lies outside Q.
(ii) P'∩Q∩R': the part of Q that is outside both P and R (Q only).
Explanation
Find d first by subtracting the two term equations.