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Answer :
Sure! Let's go through each question step-by-step.
1. What is the missing term in the sequence?
Sequence: 82, 77, __, 67, 62
To find the pattern, look at the differences between consecutive terms:
- 77 - 82 = -5
- __ - 77 = -5 (so the missing term should be 72)
- 67 - 72 = -5
- 62 - 67 = -5
Thus, the sequence decreases by 5 each time. The missing term is 72.
2. What is the rule in finding the nth term in the sequence?
Sequence: 4, 9, 16
Notice the numbers are perfect squares:
- 2² = 4
- 3² = 9
- 4² = 16
Therefore, the rule for the nth term is n².
3. What is the missing term in:
Sequence: [tex]\( \frac{1}{10}, \frac{3}{10}, \frac{5}{10}, \frac{9}{10} \)[/tex]
Look at the pattern in the numerators: they seem to be increasing by odd numbers:
- 1 to 3 is +2
- 3 to 5 is +2
- 5 to 9 is +4, continuing with this pattern the next increment is also +4
- Hence, 5 + 4 = 9, which fits the 9 already in the sequence.
The full sequence confirms the term should be [tex]\(\frac{9}{10}\)[/tex], but it is already given. If you need another slot (before completion), consider there may be a logical error or possibly a writing/presentation mistake.
4. What is the missing term in the sequence?
Sequence: 4, 7, 12, 19, __
The differences between the terms are:
- 7 - 4 = 3
- 12 - 7 = 5
- 19 - 12 = 7
The differences themselves increase by 2 each time. The next difference should then be 7 + 2 = 9. Thus, the missing term is 19 + 9 = 28.
5. What is the next letter in the sequence?
Sequence: A, F, K, P, __
Investigating the pattern of the sequence using the positions in the alphabet:
- A is the 1st letter
- F is the 6th letter
- K is the 11th letter
- P is the 16th letter
Each letter increases by 5 positions. Thus, after P (16), the next letter is:
- 16 + 5 = 21, which corresponds to the 21st letter, U.
The next letter is U.
1. What is the missing term in the sequence?
Sequence: 82, 77, __, 67, 62
To find the pattern, look at the differences between consecutive terms:
- 77 - 82 = -5
- __ - 77 = -5 (so the missing term should be 72)
- 67 - 72 = -5
- 62 - 67 = -5
Thus, the sequence decreases by 5 each time. The missing term is 72.
2. What is the rule in finding the nth term in the sequence?
Sequence: 4, 9, 16
Notice the numbers are perfect squares:
- 2² = 4
- 3² = 9
- 4² = 16
Therefore, the rule for the nth term is n².
3. What is the missing term in:
Sequence: [tex]\( \frac{1}{10}, \frac{3}{10}, \frac{5}{10}, \frac{9}{10} \)[/tex]
Look at the pattern in the numerators: they seem to be increasing by odd numbers:
- 1 to 3 is +2
- 3 to 5 is +2
- 5 to 9 is +4, continuing with this pattern the next increment is also +4
- Hence, 5 + 4 = 9, which fits the 9 already in the sequence.
The full sequence confirms the term should be [tex]\(\frac{9}{10}\)[/tex], but it is already given. If you need another slot (before completion), consider there may be a logical error or possibly a writing/presentation mistake.
4. What is the missing term in the sequence?
Sequence: 4, 7, 12, 19, __
The differences between the terms are:
- 7 - 4 = 3
- 12 - 7 = 5
- 19 - 12 = 7
The differences themselves increase by 2 each time. The next difference should then be 7 + 2 = 9. Thus, the missing term is 19 + 9 = 28.
5. What is the next letter in the sequence?
Sequence: A, F, K, P, __
Investigating the pattern of the sequence using the positions in the alphabet:
- A is the 1st letter
- F is the 6th letter
- K is the 11th letter
- P is the 16th letter
Each letter increases by 5 positions. Thus, after P (16), the next letter is:
- 16 + 5 = 21, which corresponds to the 21st letter, U.
The next letter is U.
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