First, we need to determine the common difference (d) between consecutive terms in the arithmetic sequence. Using the formula:
aₙ = a₁ + (n - 1)d
We are given: a₁ = 2, a₅ = 50, and n = 5. Plugging in the values:
50 = 2 + (5 - 1)d
48 = 4d
Now we solve for d:
d = 12
To find the sum of the terms in a finite arithmetic sequence, we can use the formula:
Sₙ = n * (a₁ + aₙ) / 2
Since we have d = 12 and want to find the sum for the first 10 terms, we need to find a₁₀:
a₁₀ = a₁ + (n - 1)d
a₁₀ = 2 + (10 - 1) * 12
a₁₀ = 2 + 108
a₁₀ = 110
Now we can calculate the sum:
S₁₀ = 10 * (2 + 110) / 2
S₁₀ = 10 * 112 / 2
S₁₀ = 5 * 112
So, the sum of the first 10 terms of this arithmetic sequence is 560. The correct answer is 560.