Respuesta :

The value for the missing term is -175.

Answer: [tex]\pm175[/tex]

Step-by-step explanation:

The given geometric sequence = [tex]35,_,875,...[/tex]

For a geometric sequence, the nth term is given by the formula

[tex]a_n=ar^{n-1}[/tex]

Since, the first term [tex]a_1=a=35[/tex]

Then, the third term =[tex]a_3=ar^2=35r^2[/tex]

From the given sequence, the third term =875

Now, [tex]\Rightarrow 35r^2=875\\\Rightarrow r^2=25\\\Rightarrow\ r=\pm5[/tex]

If r=5, then the second term =[tex]a_2=ar=35(5)=175[/tex]

If r=-5, then the second term =[tex]a_2=ar=35(-5)=-175[/tex]

Hence, the possible value for the missing term of the geometric sequence is [tex]\pm175[/tex]

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