Question

A guy initially had 1 rupee. At the end of some month n, the amount of money he had was

n2 more than three times of what he had in the previous month. Write the recurrence

equation and solve it using generating function. Find the amount of he will have at the end

of 10 months.

Answer 1

The guy initially had than the end of one rupee. At 3 times of what month he had D Moye he had previous month Write recurrence relation and solve it function. Find the using generating 10months amount the end solution : Initially he had I rupee first month month (n) 1 at end of month n an amount month Amount can) 1 had n² 2 3 times than what more end At the he of in month n he previous month had n² +3 (an-1) Recurrence relation

So de Veyse direction similarly by going in ant = (2-1)² + 31an-2] recuyence Substitute relation ana) an-2 an-3 an= n2+ 3 [(n-1) + 3 [an-2]] Similarly for anan+ 3 [o-o* + 3 [n-21] Tan= n² +3 (0-13² +32 (0-2) +33 (n-3)? .... n-1 GENERATING FUNCTION 10th month n10 At the end of 2,0° 10'+3x9 +3+x8+ 33 x 72 88507 supees lao