How many terms are in the geometric sequence having a first term of 2, a last term of 32, and a common ratio of -2?

3

Step-by-step explanation:

first term a= 2

last term tn= 32

common ratio r= -2

number of terms

= tn=ar^n-1

32 = 2*(-2)^n-1

divide both sides by 2

32/2 = 2*(-2)^n-1/2

16 = (-2)^n-1

Then...use 16 in the power of 2

(-2)^4 = (-2)^n-1

The bases (-2), cancels out

so we have: 4 = n-1

collect like terms

4-1 = n

3 = n

n= 3

yes

step-by-step explanation:

yes