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. If the expressions x + 5, 2x, and 4x −17 represent the first three terms of an arithmetic sequence, then determine the numerical value of the 20th term.

If the expressions x 5 2x and 4x 17 represent the first three terms of an arithmetic sequence then determine the numerical value of the 20th term class=

Respuesta :

Answer: The value of 20th term is 150.

Step-by-step explanation:

Since we have given that

[tex]x+5,2x,4x-17[/tex]

Since they are in AP.

So, we know that

[tex]2b=a+c\\\\2(2x)=x+5+4x-17\\\\4x=5x-12\\\\4x-5x=-12\\\\-x=-12\\\\x=12[/tex]

So, the first term would be :

[tex]x+5=12+5=17=a[/tex]

common difference would be :

[tex]2x-(x+5)\\\\=2x-x-5\\\\=x-5\\\\=12-5\\\\=7[/tex]

So, the value of 20th term would be :

[tex]a_{20}=a+19d=17+19\times 7=17+133=150[/tex]

Hence, the value of 20th term is 150.

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