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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?

1 Answer

1 vote

Answer:

a) x = 7.5

b) 15, 11.5, 8

c) -3.5

Explanation:

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


a_3-a_2=a_2-a_1

Given:


  • a_1=2x

  • a_2=x+4

  • a_3=2x-7

Therefore:


\implies a_3-a_2=a_2-a_1


\implies (2x-7)-(x+4)=(x+4)-2x


\implies 2x-7-x-4=x+4-2x


\implies x-11=-x+4


\implies 2x=15


\implies x=7.5

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


  • a_1=2(7.5)=15

  • a_2=(7.5)+4=11.5

  • a_3=2(7.5)-7=8

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


\implies d=a_3-a_2= 8 - 11.5 = -3.5


\implies d=a_2-a_1= 11.5-15 = -3.5

Therefore, the common difference is -3.5

User Zheng Qsin
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