Tags » Arithmetic Progression

Sum of 1 to n, n² or n³

We will derive summation of series with increasing difficulty.

Lets derive the simplest series summation formulas,

To derive a formula to this series consider adding the same series with all numbers reversed, that is and so on till i.e, check the following equations, 157 more words

Derive Formula

Three numbers in A.P. whose sum is a 6-th power




Find three numbers in arithmetical progression whose sum is a 6-th power.



















25 more words

Number Puzzles

Triangle(a,b,c); a^2, b^2, c^2 and cot of interior angles are in A.P.

Let be the sides of triangle such that are in A.P.

Prove that the cotangent of the interior angles are also in A.P.




















27 more words

Number Puzzles

To make {(a+b-c), (a+c-b), (b+c-a)} all squares, (a,b,c) in AP


Find three numbers in arithmetic progression such that

(1)
(2)
(3)


, ,
where the common difference is

(1) ………..
(2) ………..
(3) ………..

, , are in A.P., that is, … 69 more words

Number Puzzles

a^2 - 1, b^2 - 1, c^2 - 1 in arithmetical progression



We want , , to be in arithmetical progression

and the sum to be a square number


Here are the first few solutions:

(14, 26, 34) 38 more words

Number Puzzles

Integers (a,b,c) whose squares form an A.P. --- Part 2

In part 1, I started a discussion on the ordered triples of integers whose squares form an arithmetic progression.

In other words,
, or equivalently… 113 more words

Number Puzzles

Integers (a,b,c) whose squares form an arithmetic progression --- Part 1



Let’s look at ordered triples of integers whose squares form an arithmetic progression.

In other words,
, or equivalently

The solutions are of the form… 66 more words

Number Puzzles