From the sequence {4,10,16, ...}, we are given the following values:
the first term = 4
the common difference = 6
Since the sum of the terms is known, we let = 990. The number of terms is unknown, so we have to solve for it using the formula for the arithmetic series:
Now we have to equate each of the two factors to zero to find the value of .
It is apparent that the number of terms must be a counting number, thus is the answer.
Check:
Let's check if the number of terms of the given sequence sum up to 990.
Answers & Comments
✎ Arithmetic Series
» 18 terms of the given sequence sum up to 990.
Solution:
From the sequence {4, 10, 16, ...}, we are given the following values:
Since the sum of the terms is known, we let = 990. The number of terms is unknown, so we have to solve for it using the formula for the arithmetic series:
Now we have to equate each of the two factors to zero to find the value of .
It is apparent that the number of terms must be a counting number, thus is the answer.
Check:
Let's check if the number of terms of the given sequence sum up to 990.
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