What is the sum of the first 10 terms of the sequence defined by an = 2n + 3?

To find the sum of the first 10 terms of the sequence defined by a_n = 2n + 3, we first need to calculate the individual terms of the sequence for n = 1 to n = 10.

• For n = 1: a₁ = 2(1) + 3 = 5
• For n = 2: a₂ = 2(2) + 3 = 7
• For n = 3: a₃ = 2(3) + 3 = 9
• For n = 4: a₄ = 2(4) + 3 = 11
• For n = 5: a₅ = 2(5) + 3 = 13
• For n = 6: a₆ = 2(6) + 3 = 15
• For n = 7: a₇ = 2(7) + 3 = 17
• For n = 8: a₈ = 2(8) + 3 = 19
• For n = 9: a₉ = 2(9) + 3 = 21
• For n = 10: a₁₀ = 2(10) + 3 = 23

Now, we have the first 10 terms as follows:

5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Next, we calculate their sum:

Sum = 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

When we add these values together, we get:

• 5 + 7 = 12
• 12 + 9 = 21
• 21 + 11 = 32
• 32 + 13 = 45
• 45 + 15 = 60
• 60 + 17 = 77
• 77 + 19 = 96
• 96 + 21 = 117
• 117 + 23 = 140

Therefore, the sum of the first 10 terms of the sequence is 140.