Mathematics

The nth term of the sequence 3/2, 3, 7, 16, 35, 74 ….. is

The nth term of the sequence 3/2, 3, 7, 16, 35, 74 ….. is
  • A.
    5 . 2n-2 – n
  • B.
    5 . 2n-2 – (n+1) / 2
  • C.
    3 . 2n-2
  • D.3/2 n
Correct Answer: Option A
Explanation

3/2, 3, 7, 16, 35, 74, ….
Using the method of substitution
When n = 1, 5 . 2n-2 – 1 = 5 . 21-2 – 1
= 5 x 2-1 – 1
= 5 x 1/2 – 1
= 5/2 – 1 = 3/2
When n = 1, 5 . 2n-2 – n
= 5 . 22-2 – 2
= 5 x 20 – 2
= 5 x 1 – 2 = 3
When n = 3, 5 . 2n-2 – n
= 5 . 23-2 – 3
= 5 x 21 – 3
= 5 x 2 – 3
= 10 -3 = 7
When n = 4, 5 . 2n-2 – n
= 5 . 24-2 – 4
= 5 x 22 – 4
= 5 x 4 – 4
= 20 – 4 = 16
When n = 5, 5 . 2n-2 – n
= 5 . 25-2 – 5
= 5 x 23 – 5
= 5 x 8 – 5
= 40 – 5
= 35
When n = 6, 5 . 2n-2 – n
= 5 . 26-2 – 6
= 5 x 24 – 6
= 5 x 16 – 6
= 80 – 6 = 74
∴ 5 . 2n-2 – 1 = 3/2, 3, 7, 16, 35, 74