In order to write expressions in summation notation, you need to find the general formula for the terms and the starting and ending term of it.
For the first expression, the terms in the expression are multiples of 5, so the general term is It starts at (lower limit) and ends at or (upper limit).
For the second expression, the terms in the expression are powers of 3 (you can notice that easily as 9 = 3², 27 = 3³, 81 = 3⁴), so the general term is It starts at and ends at or
For the third expression, the terms form an arithmetic sequence with common difference of 4 and has 3 as the initial term. The general formula for the arithmetic sequence is
Answers & Comments
1. 5 + 10 + 15 + ... + 50
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2. 9 + 27 + 81 + ... + 6561
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3. 3 + 7 + 11 + ... + 39
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In order to write expressions in summation notation, you need to find the general formula for the terms and the starting and ending term of it.
For the first expression, the terms in the expression are multiples of 5, so the general term is
It starts at
(lower limit) and ends at
or
(upper limit).
For the second expression, the terms in the expression are powers of 3 (you can notice that easily as 9 = 3², 27 = 3³, 81 = 3⁴), so the general term is
It starts at
and ends at
or ![n=8. n=8.](https://tex.z-dn.net/?f=n%3D8.)
For the third expression, the terms form an arithmetic sequence with common difference of 4 and has 3 as the initial term. The general formula for the arithmetic sequence is
It starts at
and ends at
or ![n=10. n=10.](https://tex.z-dn.net/?f=n%3D10.)
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