Question

What is a possible value for the missing term of the geometric sequence 35,_,875,...

Answer 1

The value for the missing term is -175.

Answer 2

Answer:
`\pm175`

Explanation:

The given geometric sequence =
`35,_,875,...`

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

`a_n=ar^(n-1)`

Since, the first term
`a_1=a=35`

Then, the third term =
`a_3=ar^2=35r^2`

From the given sequence, the third term =875

Now,
`\Rightarrow 35r^2=875\\\Rightarrow r^2=25\\\Rightarrow\ r=\pm5`

If r=5, then the second term =
`a_2=ar=35(5)=175`

If r=-5, then the second term =
`a_2=ar=35(-5)=-175`

Hence, the possible value for the missing term of the geometric sequence is
`\pm175`