Which of these are arithmetic sequences?

A sequence of numbers is said to arithmetic if any couple of adjacent terms differ by the same number. That number is said to be the common difference of the sequence. Let's see what the differences are for each sequence:

First sequence

Difference between the first two terms:

Difference between the third and second terms:

Difference between the fourth and third terms:

The difference is constant, so this sequence is an arithmetic sequence.

Second sequence

Difference between the first two terms:

Difference between the third and second terms:

The difference is not constant, so this sequence is not an arithmetic sequence.

Third sequence

Difference between the first two terms:

Difference between the third and second terms:

The difference is not constant, so this sequence is not an arithmetic sequence.

Fourth sequence

Difference between the first two terms:

Difference between the third and second terms:

Difference between the fourth and third terms:

The difference is constant, so this sequence is an arithmetic sequence.

26

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.