Answer:
4920.
Explanation:
To find the sum of the arithmetic series 3 + 9 + 15 + 21 + ... + 243, we can identify the pattern and then use the formula for the sum of an arithmetic series.
In this series, the common difference between consecutive terms is 6. The first term, a₁, is 3, and the last term, aₙ, is 243. We want to find the sum of all the terms from the first term to the last term.
The formula for the sum of an arithmetic series is:
Sₙ = (n/2) * (a₁ + aₙ)
where Sₙ is the sum of the first n terms, a₁ is the first term, aₙ is the last term, and n is the number of terms.
In this case, we need to find the value of n, the number of terms. We can use the formula for the nth term of an arithmetic series to solve for n:
aₙ = a₁ + (n - 1)d
Substituting the known values:
243 = 3 + (n - 1) * 6
Simplifying the equation:
243 = 3 + 6n - 6
240 = 6n - 3
243 = 6n
n = 243 / 6
n = 40.5
Since n should be a whole number, we can take the integer part of 40.5, which is 40. This tells us that there are 40 terms in the series.
Now we can substitute the known values into the formula for the sum:
Sₙ = (n/2) * (a₁ + aₙ)
= (40/2) * (3 + 243)
= 20 * 246
= 4920
Therefore, the sum of the series 3 + 9 + 15 + 21 + ... + 243 is 4920.