What is the value of the 100th term in the sequence 3x+2y, 5x^2+5y^3,7x^3+8y^5...?
$${\mathtt{201}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{100}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{299}}{\mathtt{\,\times\,}}{{\mathtt{y}}}^{{\mathtt{199}}}$$
It is easier if you take the arithmetic sequence of each number individually. For instance, the first coefficients 3 and 5. You can see that the difference is 2.
For the arithmetic sequence, since a constant amount is added to each progression use:
An=A1+2(100-1) ;A1 would be the beginning term.
$${\mathtt{201}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{100}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{299}}{\mathtt{\,\times\,}}{{\mathtt{y}}}^{{\mathtt{199}}}$$
It is easier if you take the arithmetic sequence of each number individually. For instance, the first coefficients 3 and 5. You can see that the difference is 2.
For the arithmetic sequence, since a constant amount is added to each progression use:
An=A1+2(100-1) ;A1 would be the beginning term.
