We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: , where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
The degree of a polynomial is the highest exponent or sum of exponents of the variables in the individual terms of a polynomial.
Looking at each the polynomial:
3x5 + 8x4y2 – 9x3y3 – 6y5: Degree is 6 (look at the 2nd and 3rd term)
2xy4 + 4x2y3 – 6x3y2 – 7x4: Degree is 5 (look at 1st, 2nd, and 3rd term)
8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4: Degree is 6 (look at 1st term)
–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5: Degree is 6 (look at 1st and last term)
Therefore, the answer is the second option:
2xy4 + 4x2y3 – 6x3y2 – 7x4
-1 1/5 + 3/4 = -0.45
1/5 is 0.2 in decimal form, and 3/4 is 0.75:
-1.2 + 0.75 = -0.45
Hope this helps!