How do you find the sum of the first 30 terms of the arithmetic sequence 6, 13, 20, 27, 34?

by

To find the sum of the first 30 terms of the given arithmetic sequence, we can use the formula for the sum of the first n terms of an arithmetic sequence:

Sum (Sn) = (n/2) * (2a + (n-1)d)

Where:

  • Sn = Sum of the first n terms
  • n = Number of terms
  • a = First term of the sequence
  • d = Common difference between the terms

From the sequence 6, 13, 20, 27, 34:

  • The first term (a) is 6.
  • The common difference (d) can be found by subtracting the first term from the second term: d = 13 – 6 = 7.
  • The number of terms (n) we want to sum is 30.

Now, plug these values into the formula:

S30 = (30/2) * (2 * 6 + (30 – 1) * 7)

Calculating step-by-step:

  1. Evaluate (30/2):
    • 30 / 2 = 15
  2. Now calculate (2 * 6 + (30 – 1) * 7):
    • Calculate 2 * 6 = 12
    • Calculate (30 – 1) * 7 = 29 * 7 = 203
    • Add them together: 12 + 203 = 215
  3. Now plug it back into the sum formula:
    • S30 = 15 * 215
    • Finally, calculate 15 * 215 = 3225

Therefore, the sum of the first 30 terms of the sequence is 3225.

Leave a Comment