yubrajnathmrx
yubrajnathmrx yubrajnathmrx
  • 13-09-2022
  • Mathematics
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x - 1, x + 2 and 3x are the first three terms of an arithmetic sequence, find the first term and the fifth term by extracting the value of x.​

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LammettHash
LammettHash LammettHash
  • 13-09-2022

Since they're in arithmetic progression, the difference between consecutive terms is fixed.

[tex](x + 2) - (x - 1) = 3[/tex]

[tex]3x - (x + 2) = 2x - 2 = 3 \implies 2x = 5 \implies x = \dfrac52[/tex]

Then the first term is

[tex]x-1=\dfrac52 - 1 = \boxed{\dfrac32}[/tex]

and the fifth term is

[tex]3x + 3 + 3 = 3\cdot\dfrac32 + 3 + 3 = \boxed{\dfrac21}2[/tex]

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