# How do you find the sum of the arithmetic sequence given a1=3, d=-4, n=8?

The sum to n terms of an arithmetic sequence is.

here a = 3 , d =- 4 and n = 8

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To find the sum of an arithmetic sequence, you can use the formula:

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

Where:

- ( S_n ) is the sum of the first ( n ) terms of the sequence.
- ( a_1 ) is the first term of the sequence.
- ( a_n ) is the ( n )-th term of the sequence.
- ( n ) is the number of terms in the sequence.

Given:

- ( a_1 = 3 ) (the first term)
- ( d = -4 ) (the common difference)
- ( n = 8 ) (the number of terms)

We first need to find the ( n )-th term of the sequence (( a_n )) using the formula for the ( n )-th term of an arithmetic sequence:

[ a_n = a_1 + (n - 1)d ]

Substitute the given values:

[ a_n = 3 + (8 - 1)(-4) ]

[ a_n = 3 + 7(-4) ]

[ a_n = 3 - 28 ]

[ a_n = -25 ]

Now, we can plug ( a_1 = 3 ), ( a_n = -25 ), and ( n = 8 ) into the formula for the sum of the arithmetic sequence:

[ S_8 = \frac{8}{2}(3 + (-25)) ]

[ S_8 = \frac{8}{2}(3 - 25) ]

[ S_8 = \frac{8}{2}(-22) ]

[ S_8 = 4(-22) ]

[ S_8 = -88 ]

Therefore, the sum of the arithmetic sequence given ( a_1 = 3 ), ( d = -4 ), and ( n = 8 ) is ( -88 ).

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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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