+157 I don't know if the latex will work, so sorry in advance.
1. Given \($a_0 = 1$\) and \($a_1 = 5,$\), and the general relation \(a_n^2 - a_{n - 1} a_{n + 1} = (-1)^n \) for \($n \ge 1,$\) find \($a_3.$\)
2. A sequence \($\{a_n\}$\) satisfies \($a_1 = 1$\) and \(a_n = \frac{a_{n - 1}}{1 + a_{n - 1}}\) for all \($n \ge 2.$\) Find \($a_{10}.$\)
3. The first term of a sequence is 13. Starting with the second term, each term is the sum of the cubes of the digits in the previous term. For example, the second term is \($1^3 + 3^3 = 28.$\) Find the 100th term.
Thanks for the help in advance!
3 - n=13;s=0;p=0;c=1;printc," - ",n;cycle: s=(n%10);p=p+s^3;n=int(n/10);if(n!=0, goto cycle,0);c++;printc," - ",p;n=p;p=0;if(c<=100, goto cycle, 0);printc," - "
OUTPUT =:
1 - 13
2 - 28
3 - 520
4 - 133
5 - 55
6 - 250
7 - 133
8 - 55
9 - 250
10 - 133.....................So, the 100th term = 133
