Question

A blogger starts a social media campaign with an initial post that reaches 100 viewers on the first day. assume that the viewership of each successive post increases by 50% daily due to sharing and the campaign runs for n days. the total reach over the n days is represented by a finite geometric series. clearly justify your answers and show your work. a. write the finite geometric series that represents the total viewership over the 10 days. b. find the common factor a and the constant ratio r for your geometric series. c. calculate the sum of the series to find the total viewership reached by day 150 of the campaign

Answer 1

The geometric series representing the social media campaign's viewership uses the formula S = a * (1 - r^n) / (1 - r), with 'a' as 100 and 'r' as 1.5 for a 50% daily increase. The sum of viewership over 10 days forms a finite geometric series, and the total viewership by day 150 can be found using the sum of the series.

Step-by-step explanation:

To represent the total viewership over 10 days for a social media campaign as a geometric series, when the number of viewers increases by 50% each day starting with 100 viewers, we use the formula for a geometric series S = a * (1 - r^n) / (1 - r), where 'S' is the sum of the series, 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.

A. The first term 'a' for day 1 is 100 viewers, and the common ratio 'r' is 1.50 since the viewership increases daily by 50%. The finite geometric series for 10 days is 100 + 150 + 225 + ... + 100*(1.5)^(9).

B. The common factor 'a' is 100 and the common ratio 'r' is 1.5.

C. To find the total viewership by day 150 of the campaign, we calculate the sum of the first 150 terms of this geometric series. The sum S can be found using the formula provided earlier.