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

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Understanding the Sequence

The sequence defined by the formula an = 2n + 3 generates terms based on the value of n. Here, n represents the position of the term in the sequence, and we can calculate individual terms by substituting different values of n.

Calculating the Terms

Let’s calculate the first 10 terms of the sequence:

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

Sum of the Terms

Now that we have the first 10 terms of the sequence:

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

We can sum these terms together:

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

Calculating the total, we get:

Sum = 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

Final Result

Therefore, the sum of the first 10 terms of the sequence defined by an = 2n + 3 is 140.

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