The sum of the 1st and 2nd terms of an A P is 4... - WAEC Mathematics 1994 Question

\(T_{n} = a + (n - 1) d\) (terms of an A.P)

\(T_{1} = a\)

\(T_{2} = a + d\)

\(T_{10} = a + 9d\)

\(a + a + d = 2a + d = 4 ... (i)\)

\(a + 9d = 19 ... (ii)\)

(ii) x 2: \(2a + 18d = 38 ... (iii)\)

(iii) - (i) : \(17d = 34 \implies d = 2\) 

\(2a + 2 = 4 \implies 2a = 2\)

\(a = 1\)

\(T_{5} + T_{6}\)

= \((a + 4d) + (a + 5d)\)

= \(2a + 9d\)

= \(2(1) + 9(2)\)

= 20