Hi Randy,

The negative in front of the one-half is a problem.

If a is any positive real number and b is any real number then a^b is positive. Hence the left side of the equation

2¹⁰ = -1/2^x - 1

is positive and the right side is negative. Thus there is no x that makes the equation valid so there is no solution.

Harley

Randy wrote back.

I asked a question last week but you misinterpreted the question. Here it is again.

This is from an geometric sequence, where you are asked to find the number of terms.

2¹⁰ = -1/2^(n-1)

It comes from the question: Identify what term 1/32 is in the given geometric sequence 32, -16, 8, ...

The solution is n=11, but I can't seem to find an explanation for the negative in front of the 1/2.

Randy,

There should be a bracket around the -1/2 as it is the common ratio.

You are starting at 2⁵ and succesively multiplying by -1/2 andyou want to know how many times you have to do this to get to 1/32 = 1/2⁵.

Thus what is k so that (2⁵)((-1/2))^k = 1/2⁵?

Equivalently ,

solve 2¹⁰ = 1/[(-(1/2)^k] = 2^k

so k=10 and the term you're after is the 11th term.

Penny

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