The first term in a geometric sequence is -14 The common ratio is ½ What is the 5th term in the sequence?

Answer 1

first you need to write your equation.

This is an exponential function so the equation would be- A(N)=a(b)^n-1 where a is the first term in the sequence (for you a=-14) b is the common ratio (for you b=1/2) and n= the number of term in your sequence (for you n=5, but it can be any number you want to find the nth sequence of.)

Now take the equation a(n)=a(b)^n-1 and plug in your variables-

Now your equation is

a(5)=-14(1/2)^5-1

The first step to solving this is simplifying your exponent- so subtract 1 from five

then your equation would read

a(5)=-14(1/2)^4

Now solve the exponent

then you would have

a(5)=-14(1/16)

then all you have to do is multiply

a(5)=-7/8

So the fifth term in your sequence is -7/8

I hope this helped. :)