The nth term of the sequence 3 2 3 7 16 35 74 is - JAMB Mathematics 2007 Question

³/₂, 3, 7, 16, 35, 74, ....

Using the method of substitution

When n = 1, 5 . 2^n-2 - 1 = 5 . 2^1-2 - 1

= 5 x 2^-1 - 1

= 5 x ¹/₂ - 1

= ⁵/₂ - 1 = ³/₂

When n = 1, 5 . 2^n-2 - n

= 5 . 2^2-2 - 2

= 5 x 2⁰ - 2

= 5 x 1 – 2 = 3

When n = 3, 5 . 2^n-2 - n

= 5 . 2^3-2 - 3

= 5 x 2¹ - 3

= 5 x 2 – 3

= 10 -3 = 7

When n = 4, 5 . 2^n-2 - n

= 5 . 2^4-2 - 4

= 5 x 2² - 4

= 5 x 4 – 4

= 20 – 4 = 16

When n = 5, 5 . 2^n-2 - n

= 5 . 2^5-2 - 5

= 5 x 2³ - 5

= 5 x 8 – 5

= 40 – 5

= 35

When n = 6, 5 . 2^n-2 - n

= 5 . 2^6-2 - 6

= 5 x 2⁴ - 6

= 5 x 16 – 6

= 80 – 6 = 74

∴ 5 . 2^n-2 - 1 = ³/₂, 3, 7, 16, 35, 74