Determine the 8th term in the geometric sequence whose first term is -10 and has a ratio of 2

Question

Determine the 8th term in the geometric sequence whose first term is -10 and has a ratio of 2

Answer 1

A_n = A₀ * r^n-1 is the formula for a geometric sequence. All it really says is that we start with a seed value and keep multiplying it by the same ratio over and over, which is why we rewrite it as a power. Since the first term doesn't get changed, we have that "n-1" instead of "n".

Now, we simply plug in everything you were given and dance the night away!

A₈ = (-10) * (2)^8-1

     = (-10) * 2⁷

     = (-10) * 128

     = -1280

 

Answer 2

To determine the "nth" term in a geometric sequence:

 

a8 = ar^(n-1)

 

where "a" is the first term, and "r" is the common ratio.

 

a8 = (-10)*2^(8-1) = (-10)*(2^7)

 

Multiplying those values out will give you the 8th term.