The last term of the series x^2, x, 1,..........to 31 terms is

Answer 1

The series given is: x^2, x, 1, ............. to 31 terms.

This is an arithmetic sequence with a common difference of (x - x^2).
The first term (a) is x^2 and the common difference (d) is x - x^2.

We can find the nth term (Tn) of an arithmetic sequence using the formula:
Tn = a + (n - 1) * d

In this case, n is 31 (as there are 31 terms).

T31 = x^2 + (31 - 1) * (x - x^2)
T31 = x^2 + 30 * (x - x^2)
T31 = x^2 + 30x - 30x^2
T31 = -29x^2 + 30x

Therefore, the last term of the series x^2, x, 1, ............. to 31 terms is -29x^2 + 30x.