Question

If a₁ = 1 and a_n+1 – 3a_n + 2 = 4n for every positive integer n, then a₁₀₀ equals (CAT 2005)

• A. 3⁹⁹ – 200
• B. 3⁹⁹ + 200
• C. 3¹⁰⁰ – 200
• D. 3¹⁰⁰ + 200

Answer 1

The correct option is C 3¹⁰⁰ – 200

Option (c)

Shortcut: Double Substitution

Write each answer option in terms of n (where n=100)

3^n-1 – 2n

3^n-1 + 2n

3ⁿ - 2n

3ⁿ + 2n

Now at n=1, we should get 1. Put n=1 in the answer options and eliminate those options where you do not get 1

-1 ≠1

2 ≠1

1

5≠1 thus, the answer is option (c)