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The first three terms of an arithmetic progression are 2x, x+4, 2x - 7 respectively.
a. Find the value of x
b. Find the three terms
(6 m
c. What is the common difference?

Respuesta :

semsee45

Answer:

a)  x = 7.5

b)  15,  11.5,  8

c)  -3.5

Step-by-step explanation:

As there is a common difference between consecutive terms of an arithmetic progression, then:

[tex]a_3-a_2=a_2-a_1[/tex]

Given:

  • [tex]a_1=2x[/tex]
  • [tex]a_2=x+4[/tex]
  • [tex]a_3=2x-7[/tex]

Therefore:

[tex]\implies a_3-a_2=a_2-a_1[/tex]

[tex]\implies (2x-7)-(x+4)=(x+4)-2x[/tex]

[tex]\implies 2x-7-x-4=x+4-2x[/tex]

[tex]\implies x-11=-x+4[/tex]

[tex]\implies 2x=15[/tex]

[tex]\implies x=7.5[/tex]

Inputting the found value of x into the term expressions to find the three terms of the arithmetic progression:

  • [tex]a_1=2(7.5)=15[/tex]
  • [tex]a_2=(7.5)+4=11.5[/tex]
  • [tex]a_3=2(7.5)-7=8[/tex]

The common difference (d) is the difference between each consecutive term.  To find the common difference, subtract one term from the next term:

[tex]\implies d=a_3-a_2= 8 - 11.5 = -3.5[/tex]

[tex]\implies d=a_2-a_1= 11.5-15 = -3.5[/tex]

Therefore, the common difference is -3.5

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