In an A.P., of which a is the first term, if the sum of the first p terms is zero, show that the sum of the next q terms is `(-a(p +q)q)/(p-1)`.

In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is -112.

If the 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of the first 10 terms ?

If the sum of first n terms of an A.P. is cn^(2) then the sum of squares of these n terms is

Find a G.P. for which sum of the first two terms is -4 and the fifth term is 4 times the third term.

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p+ q) terms.

If the first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the 20th term.

Find the common difference of an A.P. whose first term is 100 and the sum of whose first six terms is five times the sum of the next six terms.

If the first term of an A.P. is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, find the sum of first 30 terms.