Final answer:
The sum of the first 20 terms of the given sequence is approximately 2.99998.
Step-by-step explanation:
To find the sum of the first 20 terms of the given sequence, we can use the formula for the sum of a geometric series.
The formula is: Sum = a(1 - r^n) / (1 - r)
Where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.
In this case, the first term is 1 and the common ratio is 2/3.
Plugging these values into the formula, we get:
Sum = 1(1 - (2/3)^20) / (1 - 2/3)
Simplifying the expression:
Sum = 1 - (2/3)^20 / (1/3)
Finally, calculating the sum:
Sum = 3(1 - (2/3)^20)
So the sum of the first 20 terms of the given sequence is approximately 2.99998.