Question

A music producer is making a list of vocalists needed to record an album. For each day of recording, a different number of vocalists are needed. The first day, six vocalists are needed. Each day after that, the number of vocalists needed doubles. The producer must pay by the day for each vocalist. To find the total price, the producer needs to know how many vocalists sang in total at the end of the 10th day. Use a series to find the sum after the 10th day.

Answer 1

Answer:

The number of vocalist sang on the end of the 10th day is 6138 vocalist.

Step-by-step explanation:

Given:

Number of vocalist needed on the first day = 6

Each day after that, the number of vocalists needed doubles

To Find:

The total number of vocalist found on the 10th day = ?

Solution:

By using the geometric series

$S_n=a1\cdot\frac{1-r^n}{1-r}$

Where

a is the first term

r is the ratio

n is the number of terms

On substituting the values

$S_{10}=6\cdot\frac{1-(2)^{10}}{1-2}$

$S_{10}=6\cdot\frac{1-(2)^{10}}{-1}$

$S_{10}=6\cdot\frac{1-1024}{-1}$

$S_{10}=6\cdot 1023$

$S_{10}=6138$

That is

The first day = 6 vocalist

Second day = 12 vocalist

third day =24 vocalist

Fourth day   =48 vocal list

Fifth day = 96 vocalist

Sixth day = 192 vocalist

Seventh day = 384 vocalist

eight day = 768 vocalist

Ninth day = 1536 vocalist

Tenth day = 3072 vocalist

So

6+12+24+48+96+192+384+768+1536+3072 = 6138 vocalist sang in total on the  end of tenth day.

Answer 2

Answer:

6,138

Step-by-step explanation:

I got it right on the test