Tags » Arithmetic Progression

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

Integers(a,b,c,d) in A.P. whose number of divisors is also in A.P.


229, 361, 493, and 625 are in arithmetic progression:

361 – 229 = 493 – 361 = 625 – 493 = 132

and the number of divisors of each is also in arithmetic progression: 84 more words

Number Puzzles