Answer :
Final answer:
The sequence 37, 98, 159, 220 is an arithmetic sequence with a common difference of 61. The explicit form of the sequence is given by the formula an = 37 + (n-1)*61, where n represents the position of the term in the sequence.
Explanation:
To find the explicit form of a sequence, you need to determine a pattern or a formula that defines the n-th term in terms of n, where n is the position of a term in the sequence. The given sequence is 37, 98, 159, 220. To determine the explicit form, let's examine the differences between terms:
- 98 - 37 = 61
- 159 - 98 = 61
- 220 - 159 = 61
We can see that the difference between successive terms is constant and equals 61. This indicates that the sequence is an arithmetic sequence with a common difference (d) of 61 and first term (a1) of 37.
The formula for the n-th term of an arithmetic sequence is an = a1 + (n-1)*d. Plugging our values into this formula gives:
an = 37 + (n-1)*61
This is the explicit form of the provided sequence. Each term in the sequence can be found by substituting the term number (n) into this formula.
