Arithmetic 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 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.

Let three positive numbers a, b c are in geometric progression, such that a, b+8 , c are in arithmetic progression and a, b+8, c+64 are in geometric progression. If the arithmetic mean of a, b, c is k, then (3)/(13)k is equal to

Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference. 12 ,\ 2,\ -8,\ -18 ,\ ... (ii) 3,\ 3,\ 3,\ 3,\ ddot (iii) p ,\ p+90 ,\ p+180 ,\ p+270 ,\ where p=(999)^(999)

(a) The nth term of a progression is (3n + 5) . Prove that this progression is an arithmetic progression. Also find its 6th term. (b) The nth term of a progression is (3 - 4n) . Prove that this progression is an arithmetic progression. Also find its common difference. (c) The nth term of a progression is (n^(2) - n + 1). Prove that it is not an A.P.

The fourth power of the common difference of an arithmetic progression with integer entries is added to the product of any four consecutive of it. Prove that the resulting sum is the squares of an integer.

The fourth power of common difference of an arithmetic progression with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer.

The sum of the first fifteen terms of an arithmetical progression is 105 and the sum of the next fifteen terms is 780. Find the first three terms of the arithmetical progression,.

In an arithmetical progression, the sum of p terms is m and the sum of q terms is also m. Find the sum of (p + q) terms.

The sum of four numbers in arithmetical progression is 48 and the product of the extremes to the product of the means as 27 to 35 Find the numbers