Arithmetic ProgressionArchive

Jul 23

A problem on arithmetic progression

An arithmetic progression (A.P.) or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13… is an arithmetic progression with common difference 2.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

and in general

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression.

Question:-

Find the 25th term of the following arithmetic progression
3, 6, 9, 12, 15, …

3, 6, 9, 12, 15, …

a = 3 , d = 3 , n = 25

Tn = a + (n − 1)d

T25 = 3 + (25 − 1)(3)

= 3 + 72

= 75

∴ the 25th term of the A.P. is 75.

For more help on this ,you can reply me.

May 14

Question on Circles to Find Length of the Chords

For determining the length of the chords in Circle, Rectangular Co ordinate System is used. According the graphical representation, radius towards right side is positive and towards left is negative.

Topic : Length of Chords in a Circle of radius r

Using definite integrals we can calculate the length of chords with some constraints.

Question : In a circle of radius r, find the average length of the chords perpendicular to the diameter [-r, r].

Solution :

Feb 09

Arithmetic Progression

Posted in Arithmetic Progression