Mathematics

The sum of the 1st and 2nd terms of an A.P. is 4 and the…

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