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Answer :
The number of terms in the arithmetic sequence from 46 to 139 is 94. This is calculated using the formula for the n-th term of an arithmetic sequence. The sequence has a common difference of 1.
Finding the Number of Terms in the Sequence
The given sequence is an arithmetic sequence where the first term (a) is 46 and the last term (l) is 139. In an arithmetic sequence, the common difference (d) is the difference between any two successive terms. Here, we can see that the common difference (d) is 1.
To find the number of terms (n) in the sequence, we can use the formula for the n-th term of an arithmetic sequence:
l = a + (n - 1) * d
Substituting the given values into the formula, we have:
139 = 46 + (n - 1) * 1
Simplifying this equation:
- 139 = 46 + (n - 1)
- 139 - 46 = n - 1
- 93 = n - 1
- n = 94
Therefore, the number of terms in the original sum 46, 47, 48, ... 138, 139 is 94.
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