The nth term of a geometric progression is `2(1.5)^(n-1)` for all values of n. Write down the value of a (the first term) and the common ratio (r).

The nth term of a geometrical progression is (2^(2n-1))/(3) for all values of n. Write down the numerical values of the first three terms and calculate the sum of the first 10 terms, correct to 3 significant figures.

In a geometric progression consisting of positive terms, each term equals the sum of the next terms. Then find the common ratio.

The nth term of a progression is 2^(n). Prove that it is G.P. Also find its common ratio.

The 4^(th), 6^(th) and the last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first term, common ratio and the number of terms of the series.

The sum of an infinite geometirc progression is 2 and the sum of the geometric progression made from the cubes of this infinite series is 24. Then find its first term and common ratio :-

The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:

The nth term of a progression is 3^(n+1) . Show that it is a G.P. Also find its 5th term.

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

The first term of an arithmetic progression is 1 and the sum of the first nine terms equal to 369 . The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. Find the seventh term of the geometric progression.

The first three terms of a geometric progression are 3, -1 and 1/3 . The next term of the progression is