Question

What is the 7th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500?

Answer 1

Answer: The correct option is (C) 62500.

Step-by-step explanation: We are given to find the 7-th term of the following geometric sequence :

4, −20, 100, . . .

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

`a_n=ar^(n-1).`

For the given geometric sequence, we have

first term, a = 4

and common ratio r is given by

`r=(-20)/(4)=(100)/(-20)=~~.~~.~~.~~=-5.`

Therefore, the 7-th term of the given geometric sequence is

`a_7=ar^(7-1)=4*(-5)^6=4* 15625=62500.`

Thus, the required 7-th term is 62500.

Option (C) is CORRECT.

Answer 2

The n-th term a[n] is given by
.. a[n] = 4*(-5)^(n -1)
Then
.. a[7] = 4*(-5)^6 = 62,500

The 3rd selection is appropriate.