What is the sum of the first 10 terms of the sequence defined by an = 4n + 3?

To find the sum of the first 10 terms of the sequence defined by a_n = 4n + 3, we first need to calculate the individual terms.

Let’s calculate the first 10 terms:

• a₁ = 4(1) + 3 = 7
• a₂ = 4(2) + 3 = 11
• a₃ = 4(3) + 3 = 15
• a₄ = 4(4) + 3 = 19
• a₅ = 4(5) + 3 = 23
• a₆ = 4(6) + 3 = 27
• a₇ = 4(7) + 3 = 31
• a₈ = 4(8) + 3 = 35
• a₉ = 4(9) + 3 = 39
• a₁₀ = 4(10) + 3 = 43

Now we can sum these terms:

Sum = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇ + a₈ + a₉ + a₁₀ = 7 + 11 + 15 + 19 + 23 + 27 + 31 + 35 + 39 + 43

Calculating this step-by-step gives:

• 7 + 11 = 18
• 18 + 15 = 33
• 33 + 19 = 52
• 52 + 23 = 75
• 75 + 27 = 102
• 102 + 31 = 133
• 133 + 35 = 168
• 168 + 39 = 207
• 207 + 43 = 250

Therefore, the sum of the first 10 terms is 250.