# How do you find the sum of the first 20 terms of the series #3+8+13+18+23+...#?

The first twenty terms have a sum of

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To find the sum of the first 20 terms of the series (3+8+13+18+23+...), use the formula for the sum of an arithmetic series:

[ S = \frac{n}{2}(a_1 + a_n) ]

Where:

- ( S ) is the sum of the series,
- ( n ) is the number of terms in the series (which is 20 in this case),
- ( a_1 ) is the first term of the series, and
- ( a_n ) is the last term of the series.

In this series:

- ( a_1 = 3 ) (the first term),
- To find ( a_n ), we use the formula for the ( n )th term of an arithmetic sequence: ( a_n = a_1 + (n - 1)d ), where ( d ) is the common difference between consecutive terms.
- Since the common difference between consecutive terms is 5 (each term increases by 5), we have ( d = 5 ).
- Now, plug in ( n = 20 ) into the formula for ( a_n ): [ a_{20} = 3 + (20 - 1) \times 5 = 3 + 19 \times 5 = 3 + 95 = 98 ]

Using the formula for the sum of an arithmetic series: [ S = \frac{n}{2}(a_1 + a_n) ] [ S = \frac{20}{2}(3 + 98) ] [ S = \frac{20}{2}(101) ] [ S = 10 \times 101 ] [ S = 1010 ]

So, the sum of the first 20 terms of the series (3+8+13+18+23+...) is 1010.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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