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]
