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What is the value of the 100th term in the sequence 3x+2y, 5x^2+5y^3,7x^3+8y^5...?

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What is the value of the 100th term in the sequence 3x+2y, 5x^2+5y^3,7x^3+8y^5...?

Guest Mar 7, 2015

#1
+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.

Guest Mar 7, 2015
#1
+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.

Guest Mar 7, 2015