Explanation

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

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