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, eight 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

6,138

Explanation:

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

Where

a is the first term

r is the ratio

n is the number of terms

On substituting the values

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

8184 vocalists sang in total

Explanation:

The number needed is ...

8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096

You can add these up to get a total of 8184, or you can use the formula for the sum of a geometric series:

Sn = a1(r^n -1)/(r -1) . . . . where a1 is the first term and r is the common ratio

S10 = 8(2^10 -1)/(2 -1) = 8(1024 -1)/1 = 8184