Answer :
To find the next term in the sequence -5, 0, 10, 25, 45,..., let's identify the pattern:
1. Find the differences between consecutive terms:
- From -5 to 0, the difference is [tex]\(0 - (-5) = 5\)[/tex].
- From 0 to 10, the difference is [tex]\(10 - 0 = 10\)[/tex].
- From 10 to 25, the difference is [tex]\(25 - 10 = 15\)[/tex].
- From 25 to 45, the difference is [tex]\(45 - 25 = 20\)[/tex].
2. Notice the pattern:
- The differences themselves form a sequence: 5, 10, 15, 20.
- This is an arithmetic sequence with a common difference of 5.
3. Determine the next difference:
- To continue the pattern of the differences (5, 10, 15, 20), the next difference would be [tex]\(20 + 5 = 25\)[/tex].
4. Calculate the next term in the original sequence:
- The last term provided is 45.
- Add the next difference to it: [tex]\(45 + 25 = 70\)[/tex].
Therefore, the next term in the sequence is 70. The correct answer is option D: 70.
1. Find the differences between consecutive terms:
- From -5 to 0, the difference is [tex]\(0 - (-5) = 5\)[/tex].
- From 0 to 10, the difference is [tex]\(10 - 0 = 10\)[/tex].
- From 10 to 25, the difference is [tex]\(25 - 10 = 15\)[/tex].
- From 25 to 45, the difference is [tex]\(45 - 25 = 20\)[/tex].
2. Notice the pattern:
- The differences themselves form a sequence: 5, 10, 15, 20.
- This is an arithmetic sequence with a common difference of 5.
3. Determine the next difference:
- To continue the pattern of the differences (5, 10, 15, 20), the next difference would be [tex]\(20 + 5 = 25\)[/tex].
4. Calculate the next term in the original sequence:
- The last term provided is 45.
- Add the next difference to it: [tex]\(45 + 25 = 70\)[/tex].
Therefore, the next term in the sequence is 70. The correct answer is option D: 70.
