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

Answer:

  8184 vocalists sang in total

Step-by-step 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