(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) \(P' \cap Q \cap R'\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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)
Source: Myschool Past Questions Archive (Record #54470)