(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 cap Q’ cap R) ; (ii) (P’ cap Q cap R’).
Explanation
(a) (T_{n} = a + (n – 1)d) (terms of an A.P)
(T_{6} = a + 5d = 35 … (1))
(T_{13} = a + 12d = 77 … (2))
(2) – (1) : (7d = 42 implies d = 6)
(a + 5(6) = 35 implies a + 30 = 35)
(a = 5)
(therefore T_{20} = a + 19d = 5 + 19(6))
= (5 + 114 = 119)
(b)