What is the sum of the first 10 terms of the sequence defined by an = 3n + 3?

To find the sum of the first 10 terms of the sequence defined by a_n = 3n + 3, we first need to determine the individual terms of the sequence.

Let’s calculate the first 10 terms:

• a₁ = 3(1) + 3 = 6
• a₂ = 3(2) + 3 = 9
• a₃ = 3(3) + 3 = 12
• a₄ = 3(4) + 3 = 15
• a₅ = 3(5) + 3 = 18
• a₆ = 3(6) + 3 = 21
• a₇ = 3(7) + 3 = 24
• a₈ = 3(8) + 3 = 27
• a₉ = 3(9) + 3 = 30
• a₁₀ = 3(10) + 3 = 33

Now we have the first 10 terms: 6, 9, 12, 15, 18, 21, 24, 27, 30, 33.

Next, we calculate the sum of these terms:

• Sum = 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 + 33
• Sum = 6 + 9 = 15
• Sum = 15 + 12 = 27
• Sum = 27 + 15 = 42
• Sum = 42 + 18 = 60
• Sum = 60 + 21 = 81
• Sum = 81 + 24 = 105
• Sum = 105 + 27 = 132
• Sum = 132 + 30 = 162
• Sum = 162 + 33 = 195

Thus, the sum of the first 10 terms of the sequence is 195.