Final answer:
Lydia attended a total of 126 births over 6 years, with the number of births attended doubling each subsequent year. We apply the geometric sequence sum formula to calculate this total.
Step-by-step explanation:
Calculating Total Births Attended by Lydia
Lydia is a childbirth assistant whose career began with attending 2 births in her first year. To find the total number of births she attended after 6 years, we need to recognize the pattern of growth in the number of births she attends each year, which is a doubling from the previous year. This is a geometric progression.
In the first year, Lydia attended 2 births. From the second year onward, the number of births she attended doubles each year. We can calculate the total number of births attended over 6 years using the formula for the sum of the first n terms of a geometric sequence, which is S_n = a(1 - r^n) / (1 - r), where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.
Applying this formula:
- First term (a) = 2 births
- Common ratio (r) = 2 (since the number doubles each year)
- Number of terms (n) = 6 years
The sum for 6 years is S_6 = 2(1 - 2^6) / (1 - 2) = 2(1 - 64) / (-1) = 2(-63) / (-1) = 126.
Therefore, Lydia attended a total of 126 births over the course of 6 years.