Complete the Arithmetic Sequence: 780, 770, 760, ...

Question

Complete the sequence:

780,770,760, 780,770,760,\ldots

Step-by-Step Solution

To solve this problem, we need to identify the pattern in the sequence and continue it accordingly.

The given sequence is: 780,770,760, 780, 770, 760, \ldots

Observe the first two terms: 780 780 and 770 770 . Notice that:

  • 770780=10 770 - 780 = -10

This indicates that each term decreases by 10. Applying the same logic to the next term:

  • 760770=10 760 - 770 = -10

Therefore, the sequence is an arithmetic sequence where each term decreases by 10 from the previous one.

To find the next three terms, subtract 10 from the last given term, 760 760 .

  • Next term: 76010=750 760 - 10 = 750
  • Next term: 75010=740 750 - 10 = 740
  • Next term: 74010=730 740 - 10 = 730

Thus, the completed sequence is 780,770,760,750,740,730 780, 770, 760, 750, 740, 730 .

Comparing with the provided multiple-choice answers, the appropriate choice is:

750,740,730 750,740,730

Answer

750,740,730 750,740,730