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What is the sum of the first 21 terms of the series 1 + 4 + 7 + 10 + 13 + 16 …?Select one:a. 642b. 645c. 648d. 651

Question

What is the sum of the first 21 terms of the series 1 + 4 + 7 + 10 + 13 + 16 …?

Select one:

  • a. 642
  • b. 645
  • c. 648
  • d. 651
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Solution

The given series is an arithmetic series where the common difference (d) is 3 (4-1, 7-4, 10-7, etc.).

The sum (S) of the first n terms of an arithmetic series can be calculated using the formula:

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

where:

  • n is the number of terms,
  • a is the first term, and
  • d is the common difference.

Substituting the given values into the formula:

S = 21/2 * (2*1 + (21-1)*3) S = 10.5 * (2 + 60) S = 10.5 * 62 S = 651

So, the sum of the first 21 terms of the series is 651 (option d).

This problem has been solved

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