SOLUTION: Find the general rule of the sequence: 32, -16, 8, -4, ...

Question 1196057: Find the general rule of the sequence: 32, -16, 8, -4, ...
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Without more info, there could be infinitely many possible answers. See my previous post here for more details.

If we assume the sequence is geometric, then,
a = 32 = first term
r = -1/2 = common ratio
The idea is to multiply each term by -1/2

which leads to,
nth term = a*( r )^(n-1)
nth term = 32*( -1/2 )^(n-1)
Again this all hinges on the assumption we have a geometric sequence.

Let's check the answer with something like n = 3
a_n = 32*(-1/2)^(n-1)
a_3 = 32*(-1/2)^(3-1)
a_3 = 32*(-1/2)^(2)
a_3 = 32*(1/4)
a_3 = 8
We have 8 as the third term, which indeed matches with the given sequence. I'll let you check the other values.

RELATED QUESTIONS
Find the general rule of the following sequence.show your solution... (answered by ikleyn)

What is the general term for sequence 2, -4, 8, -16, 32, ... (answered by math_helper,ikleyn)

Find the general rule of the following sequence. Show your solution 1/2,2,27/8,4,... (answered by greenestamps)

Find the general rule of the following sequence. Show your solution... (answered by ikleyn)

1+2+4+8+16+32+...+65,536 Find the sum of each sequence of numbers.... (answered by KMST)

Enter the explicit rule for the geometric sequence:... (answered by stanbon)

Write the equation for the general term of the sequence {-2, 4, -8, 16 . . .... (answered by fractalier)

. Find an explicit rule for the nth term of the sequence. -4, -8, -16, -32, ... (2... (answered by t0hierry)

Find the general rule/formula of the sequence: 7, 5, 3,... (answered by math_tutor2020,ikleyn)