Question

If $a_1=1$ and $a_{n+1}-3a_n+2=4n$ for every positive integer n, then $a_{100}$ equals (CAT 2005)

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

Answer 1

The correct option is C 3¹⁰⁰ – 200

Shortcut: Double Substitution

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

$3^{n-1}-2n$

$3^{n-1}+2n$

$3^n-2n$

$3^n+2n$

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

$-1\ne 1$

$2\ne 1$

1

$5\ne 1$ thus, the answer is option (c)