Express the series 19+23+27 +31 + 35+ 39 +43 + 47 using sigma notation.

135

Step-by-step explanation:

Find the difference between the members. The difference between every two adjacent members of the series is constant and equal to 4. The sum of thUsing our example, consider the sum. This sum can be found quickly by taking the number of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 19 + 35 = 54), and The sum of the 5 members of this series is 135 dividi This series corresponds to the following straight line y=4x+19ng by 2. Of a finite arithmetic progression is called an arithmetic series.

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.

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)