Find the sum of the geometric series x³, x⁵, x⁷, … to n terms.

If a, b, c are in A.P., then show that:

(i) a²(b + c), b²(c + a), c²(a + b) are also in A.P.

(ii) b + c - a, c + a - b, a + b - c are in A.P.

(iii) bc – a², ca – b², ab – c² are in A.P.

Insert 4 A.M.s between 4 and 19.

Find k such that k + 9, k – 6 and 4 form three consecutive terms of a G.P.

If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.