An A.P. and a G.P. of positive terms have the same first term and the sum of their first, second and third terms are respectively, `1, 1/2` and 2. Show that the sum of their fourth terms is `19/2`

Find the sum of first 51 terms of an A.P. whose 2nd and 3rd terms are 14 and 18 respectively.

If S is the sum to infinite terms of a G.P whose first term is 'a', then the sum of the first n terms is

A geometrical progression of positive terms and an arithmetical progression have the same first term. The sum of their first terms is 1 , the sum of their second terms is (1)/(2) and the sum of their third terms is 2. Calculate the sum of their fourth terms.

If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.

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

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

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

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.

How many terms are there in the A.P. whose first and fifth terms are -14 and 2 respectively and the sum of the terms is 40?