The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.
- A.
11 - B.
20 - C.
21 - D.
22 - E.
24
Correct Answer: Option B
Explanation
(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