Question

5. Your class is conducting an experiment to study geometric sequences. The class forms a line. The first person takes a whole pizza divides it in half, keeps half, and hands the other half to the next person. The next people in line do the same thing with their pieces. Which portion of the whole pizza does the seventh person in line get?

A. 1/256 B. 1/64 C. 1/128 D. 1/32

Answer 1

answer is c

Explanation:

the 1st person gets 1/2 of the pizza and then the other gets half of the remainder.(
`(1)/(2)`×
`(1)/(2)`=
`(1)/(4)`) we can build an equation for geometric sequences as

`T_(n)`=
`ar^(n-1)` where n= term u want to find,a=1st term of the sequence and r=common ratio of the sequence.

u can find r by dividing the 2nd term from 1st term then u get r=
`(1)/(2)`

substitute the values for the equation

`T_(7)`=
`(1)/(2)`×
`(1)/(2)^(7-1)`

`T_(7)`=
`(1)/(2)`×(
`(1^(6) )/(2^(6) )`)

=
`(1)/(2)`×
`(1)/(64)`

=
`(1)/(128)`