Calculate the partial sum S5 for the sequence 243, 81, 27,...
A. 2
B. 313
C. 351
D. 363
To find the partial sum S5, we need to sum up the first 5 terms of the sequence:
243 + 81 + 27 + ...
The terms of the sequence are decreasing by a factor of 3 each time. So, the general formula for the nth term is:
a_n = 243/(3^(n-1))
To find the sum of the first 5 terms, we can write:
S5 = 243/(3^0) + 243/(3^1) + 243/(3^2) + 243/(3^3) + 243/(3^4)
When we simplify each term, we get:
S5 = 243 + 81 + 27 + 9 + 3
Adding these terms together, we find:
S5 = 363
So, the correct answer is D. 363.