If a and b are the roots of x2−3x+p=0 and c, d are the roots x2−12x+q=0 where a,b,c,d form a G.P. Prove that (q+p):(q−p)=17:15.
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
Fill in the blanks in the following table, given that a is the first term, d the common difference and anthe nth term of the AP:
Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively, show that S3=3(S2−S1).
The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a : b = (m+m2−n2):(m−m2−n2).